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

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Question 1199154: Consider all of the ways of ordering the 5 letters U,S,A,M,O. Suppose these are listed in a dictionary in alphabetical order, starting with AMOSU. What position In the list would USAMO be?
A. 97 B. 103 C. 109 D. 115 E. 120
(If your answer is not one of these answer choices, you should double check your work, as it is wrong.)
Click here to see answer by ikleyn(52776)

Question 1199248: Q1) A pizza shop offers three toppings: pineapple, peppers, and pepperoni. A pizza can have
0, 1, 2, or 3 toppings. What’s the probability that a random customer asks for two toppings?
Click here to see answer by greenestamps(13198)

Question 1199262: 1. In Angel’s Garden, there is a 3% chance that a tomato will be bad. Angel harvests 100
tomatoes and wants to know the probability that at most five tomatoes are bad.
2. Consider a rather nonstandard dice. Instead of the numbers 1 through 6, die A has two 3’s,
two 5’s, and two 7’s; die B has two2’s, two 4’s, and two 9’s; and die C has two 1’s, two 6’s,
and two 8’s, as in the figure below
Suppose dice A and B are rolled. If A is more likely to get the higher number. That is, P(A >
B) > 0.50, where {A > B} denotes the event that A beats B. Hint: Condition on the outcome of
die A.
Now, if B and C are rolled, B is more likely to get the higher number. And, remarkably, if C
and A are rolled, C is more likely to get the higher number. These dice are known as nontransitive dice and are the basis of a magic trick. You pick any die. Then anyone can always
pick a die that is more likely to beat yours. If you pick A, he picks C. If you pick B, he picks
A. And if you pick C, he picks B. Your task is to write an R code that will simulate this nontransitive dice elaborated above.
HINT: Define three functions that will represent the three dices as samples representing the
three configurations given in the figure above (A, B and C), then replicate the experiment
several times (100, or 1000 times) by calling the functions with the conditions given above.

Click here to see answer by ikleyn(52776)

Question 1199291: A signal can be formed by running different colored flags up a pole, one above the other. Find the number of different signals consisting of 8 flags that can be made if 3 of the flags are white, 3 are red, and 2 are blue.
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Question 1199384: 3) How many 7-character license plates are possible if the first three characters must be letters, the last four must be digits 0-9, and repeated characters are allowed?
Click here to see answer by Alan3354(69443)

Question 1199536: August is selling tickets for his school play.
-Adults pay $7 a ticket while students pay $5 a ticket.
-August sells 35 tickets and collects $160.
How many of each type of tickets did he sell?
A. 40 students and 32 adults
B. 20 students and 15 adults
C. 4 students and 5 adults
D. 15 students and 20 adults
Click here to see answer by josgarithmetic(39616)

Question 1199570: How many ways are there to arrange the first ten positive integers such that the multiples of 2 appear in increasing order, and the multiples of 3 appear in decreasing order?
Click here to see answer by greenestamps(13198)

Question 1199761: i) In how many ways six men and four women sit in a row
ii) In how many ways can they sit in a row if all the men sit together
iii) In how many ways can they sit in a row if just the women sit together
iv) In how many ways can they sit in a row if men sit together

Click here to see answer by math_tutor2020(3816)

Question 1199814: A floral arrangement consists of 6 different colored roses, 3 different colored carnations, and 3 different colored roses. You can choose from 8 different colors of roses, 6 different colors of carnations, and 7 different colors of daises. How many different arrangements are possible?
Click here to see answer by ikleyn(52776)

Question 1199915: Assume that the student has a cup with 10 writing implements: 5 pencils, 3 ball point pens, and 2 felt-tip pens.
(1) In how many ways can the student select 4 writing implements?
(2) In how many ways can the selection be made if no more than one ball point pen is selected?

Click here to see answer by greenestamps(13198)

Question 1199953: A bag of marbles contains seven purple, six gold and five white marbles. You select
four. How many ways are there to get at least three purple?

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Question 1199967: Consider the integers from 1,000 to 9,999 which have only odd digits.
a. How many of these have all different digits?
b. How many have odd digits with possible digit repetitions?
Click here to see answer by ikleyn(52776)

Question 1199982: A Mix-n-Match selection of 10 cookies is to be made from three varieties: oatmeal, peanut butter, and sugar. How many different selections are possible?
Click here to see answer by Edwin McCravy(20054)

Question 1200195: If the team has four golf clubs and they want to give only three of them to their three players. How many options are there if the number 1 golf club should be for the first player and the number 3 golf club should be for the second or third player with replacement and without replacement?
Click here to see answer by ikleyn(52776)

Question 1200300: A security code is to be chosen using 6 following letter A, B, c the number 2, 3, 5 and * and s
Click here to see answer by Alan3354(69443)

Question 1200544: A chef has 10 brands of hot sauce. In how many ways can the chef pick 3 to mix into a gumbo?
Click here to see answer by ikleyn(52776)

Question 1200667: 4. a box has 6 blue socks and 4 white socks. find the number of ways two socks
can be drawn from the box where: ว a. there are no restrictions b. they are
different colors c. there are the same color
Click here to see answer by Edwin McCravy(20054)

Question 1200678: How many three-digit numbers can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 without repetition?
Click here to see answer by Alan3354(69443)

Question 1200684: A company has 11 software engineers and 7 civil engineers. In how many ways can they be seated in a row so that no two of the civil engineers will sit together?
Click here to see answer by ikleyn(52776)

Question 1200705: In a classroom of 24 students, the teacher forms groups of 6 students each. How many different ways can these groups be formed?
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Question 1200705: In a classroom of 24 students, the teacher forms groups of 6 students each. How many different ways can these groups be formed?
Click here to see answer by greenestamps(13198)

Question 1200721: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a card greater than 3 and less than 10

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Question 1200765: A circle with centre (-3, 1) passes through the point (3, 1) find it's equation
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Question 1200763: A committee of 2 tutors and 5 pupils is to be formed among 6 tutors and 10 pupils. In how many ways can this be done, if one particular pupil must be on the committee and two particular pupils must not be on the committee
Click here to see answer by math_tutor2020(3816)

Question 1200790: A baseball team has seven colors of hats, three colors of jerseys, two colors of pants,
and five colors of shoes for uniform choice. How many different combinations of
hats, jerseys, pants, and shoes are there?
Click here to see answer by Solver92311(821)

Question 1200793: How many ways can 7 beads be placed on a bracelet with no claps?

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Question 1200793: How many ways can 7 beads be placed on a bracelet with no claps?

Click here to see answer by ikleyn(52776)

Question 1200860: Question: How many angles less than 180 degrees are formed by 12 straight lines which terminate in a point if no two of them are in the same straight line?
I have trouble understanding the question, despite reading it over and over again! Does it mean there are 12 straight lines are intersecting at one single point OR one end of the 12 lines are meeting at a point (12 lines radiating at a point)
Either answering or pointing to an illustrative question-number under Permutations and Combinations will be greatly appreciated.
Thank you
Click here to see answer by ikleyn(52776)

Question 1200864: DNA molecules include the base units adenine, thymine, cytosine, and guanine (A, T, C, and G). The sequence of base units along a strand of DNA encodes genetic information. In how many different sequences can A, T, C, and G be arranged along a short strand of DNA that has only 8 base units?
Click here to see answer by ikleyn(52776)

Question 1200865: how many ways can three awards be given to 6 students. each student may receive more than one award? each student may receive no more than one award?
Click here to see answer by ikleyn(52776)

Question 1200891: A store sells clothes for men. It has 3 kinds of jackets, 7 kinds of shirts, and 5 kinds of pants. Find the number of ways a
person can buy:
a. One of the items
b. One of each of the three kinds of clothes.
Click here to see answer by ikleyn(52776)

Question 1200685: A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that all the civil engineers do not sit together?
Click here to see answer by Edwin McCravy(20054)

Question 1200943: how many possible 5 card hands from a standard 52-card deck playing cards with one spade, two hearts and two diamonds
Click here to see answer by Alan3354(69443)

Question 1200943: how many possible 5 card hands from a standard 52-card deck playing cards with one spade, two hearts and two diamonds
Click here to see answer by Edwin McCravy(20054)

Question 1201199: How many ways to create a five card poker hand with 2 aces and 2 kings?
Click here to see answer by math_tutor2020(3816)

Question 1201199: How many ways to create a five card poker hand with 2 aces and 2 kings?
Click here to see answer by greenestamps(13198)

Question 1201241: A COMMITTEE OF 4 IS TO BE CHOSEN FROM 4 LAWYERS AND 3 ENGINERERS, FIND
IN HOW MANY WAYS THE COMMITTEE CAN BE CHOSEN.
IN HOW MANY WAYS THE COMMITTEE CAN BE EQUALLY REPRESENTED BY THE TWO PROFESSIONS
Click here to see answer by Glaviolette(140)

Question 1201252: In how many ways can 15 books be divided equally among 3 people?

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Question 1201256: a large sack contains six basketballs and five volleyballs. Find the number of ways that four balls can be selected from the sack if you must select at least two volleyballs?
Click here to see answer by greenestamps(13198)

Question 1201254: Determine the total number of divisors of the number 5880. How many are even? How many are odd?
Click here to see answer by greenestamps(13198)

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