Questions on Algebra: Combinatorics and Permutations answered by real tutors!

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Question 1194314: How many possible arrangements exist for the following:
license plates with two letters followed by four digits, or four digits followed by two letters.
Click here to see answer by ikleyn(52778)

Question 1194402: How many ten-digit phone numbers begin with the digits 212 and then have 7 distinct digits?
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Question 1194573: In how many ways can 4 people be seated in a row of 12 chairs
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Question 1194573: In how many ways can 4 people be seated in a row of 12 chairs
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Question 1194598: Let r in N such that
1 binom 9 r - 1 binom 10 r = 11 6 binom 11 r .
Find the value of r.
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Question 1194623: Find the total number of different permutations of all the letters of the word SECONDARY.
Select one:
a.
36,288

b.
362,880

c.
181,440

d.
90,720
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Question 1194665: Write an explanation for a student in Mathematics 30-1 about how to expand (a+b)^3. Fully describe two methods of expanding the power of the binomial
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Question 1194870: A man has a total of n friends, he want to invite three of them for the dinner every day during the first 4 months of the year 2023. Calculate the minimum number of friends, n, he must have if he does not want to invite the same combination of three friends more than once?
Click here to see answer by shlomitg(8)

Question 1194869: A certain country assigns motor vehicle license plates with three digits from the decimal number system followed by three uppercase letters from the English alphabet. If the letters I and O are excluded and zero cannot be the first character,
How many license plates are possible?.
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Question 1194881: How many words can be made from the word "EAMCET" if we take two vowels together?
Click here to see answer by Edwin McCravy(20054)

Question 1194941: In choosing what music to play at a charity fund raising event, Cory needs to have an equal number of symphonies from Haydn, Mendelssohn, and Mahler. If he is setting up a schedule of the 12 symphonies to be played, and he has 104 Haydn, 17 Mendelssohn, and 9 Mahler symphonies from which to choose, how many different schedules are possible? Express your answer in scientific notation rounding to the hundredths place.
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Question 1195029: How many ways are there to distribute 15 district objects into 5 distinct boxes with:
i) At least three empty box
ii) No empty box
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Question 1195072: There are 13 female board members and 17 male board members.
How many ways are there to make a committee of 18 board members?
How many ways are there to make a committee of 18 board members if exactly 7 must be female?
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Question 1195177: you have 3 pairs of pants , 4 shirts, and 2 pairs of shoes to choose from in the morning. How many different outfits are possible
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Question 1195198: Consider the numbers 0,2,5,6. How many two-digit numbers can be formed without repetition, such that.
a): all are even?
b): all are greater than 60?
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Question 1195254: Numbers are to be built using only the digits 1,2,3,4, and 5 in such a way that each digit is only used once in each number. How many of these numbers will have the following property?
(a) The first digit is divisible by one
(b) The first 2 digits make a number that is divisible by 2
(c) The first 3 digits make a number that is divisible by 3
(d) The first 4 digits make a number that is divisible by 4
(e) All 5 digits make a number that is divisible by 5
Click here to see answer by lotusjayden(18)

Question 1195298: A stock can go up,go down,or stay unchanged. How's many possibilities are there if you own 8 stocks?
Click here to see answer by math_helper(2461)

Question 1195311: How many ways can 2 purple, 3 yellow, and 2 blue bulbs be arranged in a string of Christmas tree lights with 7 socks?
Click here to see answer by ikleyn(52778)

Question 1195426: in the 6/49 lottery,six different numbers must be selected between 1 through 49 inclusive(order is not important).
1)to win the grand prize your 6 numbers must match the 6 numbers drawn. what is the probability of winning the grand prize?
Click here to see answer by Alan3354(69443)

Question 1195502: In a different plan for area codes the first digit could be any number from 2 through 6 and the second digit was either a 3 or a 4 and the third digit could be any number expect 3,4 or 8 with this plan how many differnt area codes are possible
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Question 1195513: Sara manages to shoot seven out ten baskets while practicing basketball. Based on her
practice, what is the experimental probability that she will score the next basket?
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Question 1195580: A catering service offers 8 appetizers, 9 main courses, and 7 desserts. A banquet committee is to select 3 appetizers, 5 main courses, and 3 desserts. How many ways can this be done?
Click here to see answer by ikleyn(52778)

Question 1195817: the homestyle cafe offers these combination in dinner menu
* Meat item: Sikam pa, Chicken chili, Beef curry
* Vegetables: peas, mushrooms
* salads: fruits, fresh green
*Dessert: ice cream, cake.
if you choose one item from each category, how many days can you eat meals at the homestyle cafe before u eat the same dinner second time?
Click here to see answer by ikleyn(52778)

Question 1195868: 1: A figure skating coach has 20 athletes and wishes to select 8 to take to a training trip. How many different ways could he select these 8 athletes?

2: The figure skating coach decides to enter 6 athletes into a competition. If no ties are allowed, how many different top-two orders are possible for these 6 athletes?
Click here to see answer by ikleyn(52778)

Question 1195877: How many five-letter permutations can be made from the letters in the word "ADDITION"?

Click here to see answer by greenestamps(13198)

Question 1196063: A child has three bags of fruits in which Bag 1 has 5 apples and 3 oranges, Bag 2 has 4 apples and 5 oranges and Bag 3 has 2 apples and 3 oranges. One fruit is drawn at random from one of the bags. It was an apple. Please calculate the probability that the chosen fruit was apple and was drawn from Bag 3.
Click here to see answer by math_tutor2020(3816)

Question 1196062: The test accurately indicates the disease in 98% of the people who have it, and it accurately indicates no disease in 94% of the people who do not have it. What is the false positive rate (probability of a false positive)?
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Question 1196163: how many permutations can be made from the letters in the word "MONDAY" if
a). all letters are used
b). arranged where A is the first letter
c). arranged if A, N, and D, are together
d). arranged if A, N, and D, are seperated
Click here to see answer by math_tutor2020(3816)

Question 1196161: a box contains 4 red, 3 blue, 2white balls. In how many ways can we select 3 balls such that
a). they are different colors?
b). they are all red
c). two are blue and one is white?
d). exactly 2 are blue?
e). non is white
f). at least one white?
Click here to see answer by math_helper(2461)

Question 1196248: A panel of 6 members is to be formed from 5 doctors and 10 nurses to include each profession. Find, correct to two decimal places, the probability of selecting the members to include: (a) equal doctors and nurses; (b) at most two nurses; (c) more doctors than nurses.
Click here to see answer by ikleyn(52778)

Question 1196510: a base ball team consisting of 5 boys and 4 girls will be formed from a group of 6 boys and 7 girls. find how many different teams can be formed from the group?
Click here to see answer by greenestamps(13198)

Question 1196575: In how many ways can 12 different easter eggs be distributed between 3 families if the Frankos get 5, Manchurs get 4 and the smiths get the rest?
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Question 1196637: Simplify the expression (3n-3)!/(3n+3)!
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Question 1196684: 1) There are 4 golden coins and 8 iron coins in a bag. You select one coin from the bag, if it is a golden coin, you keep it; but if it is an iron coin, you put it back in the bag. Find the probability of earning exactly 2 golden coins after:
a) Two consecutive selections
b) Three consecutive selections

Click here to see answer by greenestamps(13198)

Question 1196699: Marvin the fly starts at (0,0). For each step, Marvin moves one unit right or one unit up. He is trying to get to the point (5,7). However, at (4,4) there is a frog that will eat him if he goes through that point. In how many ways can Marvin reach (5,7)?
Click here to see answer by ikleyn(52778)

Question 1196793: At Patty the Panda's pizza parlor, the possible pizza toppings are pesto, pepperoni, peppers, and pineapple, and the possible desserts are pumpkin pie, powdered-sugar pretzels, and papaya popsicles. If Prajwal the porcupine, Petunia the peacock, and Pete the parakeet each randomly choose a subset of the pizza toppings and a dessert, what is the probability that at least two of them choose the exact same pizza or the same dessert (or both)?
Click here to see answer by ewatrrr(24785)

Question 1196820: A project team of 6 students is to be selected from a class of 20
a) How many different teams can be selected?
b) How many of the teams would include the oldest and the youngest student
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Question 1196821: Lori needs to get ready for a party. She has two types of skirts to choose from: one black and one brown. She has three blouses to choose from: one blue, one yellow and one white. Any combination of skirts and blouses is equally
likely. The probability that she will wear the white blouse and the black skirt is:
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Question 1196823: You have just been assigned a random 4-digit password made up of digits from 0 to 9. What is the probability that your password starts with a 3? Repetition is not allowed.
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Question 1196822: There are 9 people on a basketball team. The probability that you and your two best friends get to stand together in
the team picture is:
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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