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Question 1208391: One of the educational sites on the Internet requires the creation of
User account protected with 8 characters password
Different Choose from letters: A, B, C, D, E, F
And numbers: 6 , 5 , 4 , 3 , 2 , 1, find the number of passwords that
They can be created in the following cases:
The password contains 4 characters next to each other
Click here to see answer by ikleyn(52776)   |
Question 1208459: One of the educational sites on the Internet requires the creation of
User account protected with 8 characters password
Different Choose from letters: A, B, C, D, E, F
And numbers: 6 , 5 , 4 , 3 , 2 , 1, find the number of passwords that
They can be created in the following cases:
The password contains 4 numbers and 4 letters next to each other
Click here to see answer by ikleyn(52776) |
Question 1208471: One of the educational sites on the Internet requires the creation of
User account protected with 8 characters password
Different Choose from letters: A, B, C, D, E, F
And numbers: 6 , 5 , 4 , 3 , 2 , 1, find the number of passwords that
They can be created in the following cases:
The password contains 4 numbers and 4 letters combined together
Click here to see answer by greenestamps(13198)  |
Question 1208608: Pablo is putting 10 books in a row on his bookshelf. He will put one of the books, Pride and Predjudice, in the first spot. He will put another of the books, Little Women, in the last spot. In how many ways can he put the books on the shelf?
Click here to see answer by ikleyn(52776) |
Question 1208639: In a series of coin flips, a run is a series of one or more consecutive coin flips that all have the same result. For example, in the sequence
\[TT \textcolor{red}{HHH} TTHHHTH,\]
the red letters form a run of length $3$. (A run of length $1$ is still considered a run.)
If a fair coin is flipped two times, what is the expected number of runs? (If you're confused about how to count the number of runs, the example sequence above has $6$ runs.)
Click here to see answer by greenestamps(13198) |
Question 1208640: Joanna has several beads that she wants to assemble into a bracelet. There are seven beads: five of the beads have the same color, and the other two all have different colors. Using all seven beads, in how many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)
Click here to see answer by ikleyn(52776) |
Question 1208649: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
How many 7-card hands will consist of exactly 2 kings and 3 queens?
Click here to see answer by ikleyn(52776) |
Question 1208649: A standard deck of cards consists of four suits (clubs, diamonds, hearts, and spades), with each suit containing 13 cards (ace, two through ten, jack, queen, and king) for a total of 52 cards in all.
How many 7-card hands will consist of exactly 2 kings and 3 queens?
Click here to see answer by Edwin McCravy(20054)  |
Question 1208703: A standard six-sided die is rolled $8$ times. You are told that among the rolls, there was one $1$, two $2$'s, four $3$'s, and one $4$. How many possible sequences of rolls could there have been? (For example, $2,$ $1,$ $3,$ $3,$ $3,$ $2,$ $3,$ $4$ is one possible sequence.)
Click here to see answer by ikleyn(52776) |
Question 1209003: Suppose we want to choose 6 letters, without replacement, from 8 distinct letters.
How many ways can this be done, if the order of the choices does not matter?
How many ways can this be done, if the order of the choices matters?
Click here to see answer by ikleyn(52776) |
Question 1208643: We call a number cozy if every digit in the number is either a $3$ or next to a $3.$ For example, the numbers $333,$ $83,$ $303,$ and $3773$ are all cozy, but the numbers $32423,$ $786,$ $340,$ and $3999$ are not cozy.
How many positive $10$-digit numbers are cozy?
Click here to see answer by CPhill(1959)  |
Question 1208643: We call a number cozy if every digit in the number is either a $3$ or next to a $3.$ For example, the numbers $333,$ $83,$ $303,$ and $3773$ are all cozy, but the numbers $32423,$ $786,$ $340,$ and $3999$ are not cozy.
How many positive $10$-digit numbers are cozy?
Click here to see answer by ikleyn(52776) |
Question 1196898: Problem:
In the game of SET,Find the number of sets where all three cards are the same for exactly 0,1,2,3 attributes.
Background info(in case you don't know what the game set is):
In the card game Set, each card features a number of shapes, with four attributes:
Number: The number of shapes is 1, 2, or 3.
Color: Each shape is red, purple, or green.
Shape: Each shape is oval, diamond, or squiggle.
Shading: Each shape is hollow, shaded, or striped.
There is exactly one card for each possible combination of attributes.
In the game, several of the cards are dealt out, and the goal is to find a set. A set is formed by three cards, where for each attribute, either all three cards are the same, or all three cards are different.
Click here to see answer by CPhill(1959) |
Question 1207003: There are 3n children in a room, where n of them are wearing a red hat, n of them are wearing a green hat, and n of them are wearing a blue hat. These children are seated at random in a row of 3n chairs where n chairs are red, n chairs are green, and n chairs are blue. Let X_n be the number of children who sit in a chair of the same colour as their hat. (a) Find, in terms of n, the largest possible value of X_n and the probability that X_n equals that value. (b) Find E(X_n) in terms of n. (c) Show that Var(X_n)= (2n^2)/(3n-1)
[Hint: For iā{1,ā¦,3n}, define I_i as the indicator that child i has a colour match in chair and hat.]
Click here to see answer by CPhill(1959) |
Question 1205135: Student A was tasked to program an algorithm for a number generator. The generator will be used by Soda Co. for their bottlecaps.
Soda Co. will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. Those that are not winning codes are duplicated 10 times.
If Student B was to join, how many bottles of Soda will he need to buy to have a 1% chance at winning.
And if Student C would join too, what is the chance that having 24 bottlecaps have a chance at winning?
Click here to see answer by ElectricPavlov(122) |
Question 1205136: Student A was tasked to program an algorithm for a number generator. The generator will be used by A Soda Company for their bottlecaps.
Soda Company will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. Those that are not winning codes are duplicated 10 times.
If Student B, was to join, how many bottles of Soda will he need to buy to have a 1% chance at winning.
And if Student C would join too, what is the chance that 24 bottlecaps have at winning?
Click here to see answer by asinus(45) |
Question 1205063: You were tasked to program an algorithm for a number generator. The generator will be used by a soda company for their bottlecaps. The soda company will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. If a second person was to join, how many bottles of Pepsi will the 2nd person need to buy to have a 1% chance at winning.
Click here to see answer by textot(100) |
Question 1205063: You were tasked to program an algorithm for a number generator. The generator will be used by a soda company for their bottlecaps. The soda company will be holding a bottlecap lottery where 5 select bottlecaps will be winning combinations. There would be three characters printed on the bottlecaps with each character having the chance to be repeated. If a second person was to join, how many bottles of Pepsi will the 2nd person need to buy to have a 1% chance at winning.
Click here to see answer by ikleyn(52776) |
Question 1209329: Not including the identity transformation, the eleven transformations that preserve the regular hexagon shown are counterclockwise rotations by $60^\circ,$ $120^\circ,$ $180^\circ,$ $240^\circ$ and $300^\circ$ and reflections across the six dashed lines shown. Kristina randomly picks six transformations $T_1,$ $T_2,$ $T_3,$ $T_4$, $T_5$ and $T_6,$ with replacement, from this set of eleven. She performs these six transformations on the hexagon, in succession. The probability that the point $P$ is transformed to each of the hexagon's six vertices exactly once during this process is $\dfrac{k}{11^6}.$ What is the value of $k\,?$
Click here to see answer by CPhill(1959) |
Question 1209329: Not including the identity transformation, the eleven transformations that preserve the regular hexagon shown are counterclockwise rotations by $60^\circ,$ $120^\circ,$ $180^\circ,$ $240^\circ$ and $300^\circ$ and reflections across the six dashed lines shown. Kristina randomly picks six transformations $T_1,$ $T_2,$ $T_3,$ $T_4$, $T_5$ and $T_6,$ with replacement, from this set of eleven. She performs these six transformations on the hexagon, in succession. The probability that the point $P$ is transformed to each of the hexagon's six vertices exactly once during this process is $\dfrac{k}{11^6}.$ What is the value of $k\,?$
Click here to see answer by ikleyn(52776) |
Question 1193717: How many ways can 7 boys and 7 girls be seated at a round table if:
A. No restriction is imposed?
B. The girls and the boys are to occupy alternate seats?
C. 5 particular girls must sit together
D. 5 particular girls must not sit together?
E. All the girls must sit together?
Click here to see answer by proyaop(69) |
Question 1209389: In a local high school, from a group of 18 students comprised of 10 singers and 8 actors, a 5-person executive council is selected. Find how many committees are possible that have at most 2 singers.
I used (10C2)(8C3)=2520 to account for the case in which there is 2 singers and 3 actors
Than I used (8C4)(10C1)=700 to account for the case in which there is 1 singer and 4 actors
Then I used just 8C5=56 to account for the case in which there is 5 actors
Then I added them all together 2520+700+56=3276 which gives me 3276 total combinations
Click here to see answer by ikleyn(52776) |
Question 1192165: How many ways are there to choose two twos from a standard 52-card deck?
How many ways are there to choose three cards from a standard 52-card deck without choosing any twos?
How many five-card hands (drawn from a standard 52-card deck) contain exactly two twos?
How many five-card hands (drawn from a standard 52-card deck) contain a two-of-a-kind?
Click here to see answer by CPhill(1959) |
Question 1191617: A dance instructor asks each student to do 4 out of the 10 dance routines. Of the 10 dance routines, 2 are easy, 5 are moderately difficult, and 3 are difficult. In how many ways can a student select each of the following for the 4 dance routines?
a) 4 moderately difficult routines
b) 4 easy or moderately difficult routines
c) 2 moderately difficult and 2 difficult routines
d) 1 easy and 3 difficult routines
(I want detailed explanation please and thank you).
Click here to see answer by CPhill(1959) |
Question 1190992: Ten people (5 men and 5 women) are attending a dinner party. In how many ways can they be arranged if:
a. they are to be arranged in a line for a picture?
b. They are to be arranged with men and women alternating around the table?
c. they are arranged in a line for a picture but the man and women must alternate?
Click here to see answer by CPhill(1959) |
Question 1182178: Use the given confidence level and sample data to find a confidence interval for the population standard deviation o. Assume that a simple random sample has been selected from a population that has a normal distribution.
Salaries of college graduates who took a geology course in college
95% confidence; n=51, x=$60100, s=$19008
ā$____< o < $____
Click here to see answer by CPhill(1959) |
Question 1178806: Suppose you had graduated from high school but did not have enough money to continue your college education. You decided to work temporarily and save for your schooling You applied at Mr.
Agustin's restaurant and were hired. After a few days, you noticed that the restaurant business was not doing very well, and Mr. Agustin asked for your opinion. What you noticed was that there was no variety
in the food being served in the restaurant
1. Prepare a list of different choices of food that may be served (soup, meat dishes, fish,
vegetables, fruits, desserts, beverages). Consider health and nutritional values
2. Formulate and solve 2 problems involving permutation and combination concepts in the situation.
Please, I need an answer..
Click here to see answer by CPhill(1959) |
Question 1178806: Suppose you had graduated from high school but did not have enough money to continue your college education. You decided to work temporarily and save for your schooling You applied at Mr.
Agustin's restaurant and were hired. After a few days, you noticed that the restaurant business was not doing very well, and Mr. Agustin asked for your opinion. What you noticed was that there was no variety
in the food being served in the restaurant
1. Prepare a list of different choices of food that may be served (soup, meat dishes, fish,
vegetables, fruits, desserts, beverages). Consider health and nutritional values
2. Formulate and solve 2 problems involving permutation and combination concepts in the situation.
Please, I need an answer..
Click here to see answer by ikleyn(52776) |
Question 1177694: 1.) A dance instructor asks each student to do 4 out of 10 dance routines. Of the 10 dance routines, 2 are easy, 5 are moderately difficult and 3 are difficult. In how many ways can a student select each of the following for the 4 dance routines?
A. 4 moderately difficult routines
B. 4 easy or moderately difficult routines
C.2 moderately difficult and 2 difficult routines
D. 1 easy and 3 difficult routines
Click here to see answer by CPhill(1959) |
Question 1176870: You are ordering a hamburger and can get up to eight toppings, but each topping can only be used once. You tell the cashier to surprise you with the toppings you get. What is the probability that you get zero toppings? Express your answer as a fraction or decimal number rounded to four decimal places.
Click here to see answer by ikleyn(52776) |
Question 1175169: For the upcoming world-cup, the Indian Cricket Selection Committee has to come up with a possible batting order for their players. Instead of using the traditional approach they have decided to use computer algorithms to come up with all the possible batting orders and then decide from that. The
algorithm however requires the possible batting positions for each player.
The algorithm takes a list of 11 players. Each player can have more than one position they can bat at. Your job for now is to help the selection committee calculate the total number of unique batting charts such that every player gets exactly one batting position from their list of positions and no two players are given the same batting position in one batting chart.
Player / < position 1> / < position 2> / < position 3>ā¦.
Ex:
P1 / 1 / 2 / 3 / 4
P2 / 1 / 5 / 9 / 2 / 6 / 7 / 8
P3 / 1 / 2 / 7 / 10 / 3
P4 / 1 / 9 / 2 / 6 / 7 / 10 / 3 / 4
P5 / 5 / 9 / 2 / 8 / 3 / 4
P6 / 1 / 5 / 3 / 6
P7 / 6 / 7 / 4
P8 / 1 / 9 / 2 / 4
P9 / 9 / 6 / 11 / 3 / 4
P10 / 1 / 5 / 9 / 7 / 8 / 4
P11 / 6 / 11 / 7 / 10
The total number of allocations possible is: 4646.
How to arrive at this solution?
Click here to see answer by CPhill(1959) |
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Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035
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