12. How many possible sets of four marbles include no more than 1 purple marble?

Q: How many different committees are possible that consist of 5 women and 3 men selected from a group…

A: For a committee, arrangement does not matter so use the combination method.  We can select 5 women…

Q: A bowl contains 100 piece of colored candy: 28 green, 20 red, 12 yellow, 10 blue, 20 brown, and 10…

A: Given that a bowl contains 100 piece of colored candy in which 28 green, 20 red ,12 yellow, 10 blue,…

Q: Find the number of combinations that can be drawn without replacement by pulling 2 balls from a set…

A:

Q: 3. Suppose 1500 runners are in a race. How many ways could the runners finish in 1*, 2nd and 3rd…

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Q: men. How many ways are there to chc en?

A:

Q: 8. How many different mixes of candy are possible if a mix consists of 10 pieces of candy and 4…

A:

Q: 8. Twenty one boxes contain in total 200 cards. Show that at least two boxes must contain the same…

A:

Q: How many ways are there to place 13 identical red balls into 7 numbered bins?

A: Given Data: The total number of red balls is: n=13 The total number of bins is: r=7 The number of…

Q: 8. Nine people are going on a skiing trip in 3 cars that will hold 2, 3, and 4 passengers,…

A:

Q: 23. In his suitcase, Jack has 3 shirts, 4 pants, 2 socks (pairs of socks), and 2 shoes (pairs of…

A: Given: In his suitcase, Jack has 3 shirts, 4 pants, 2 socks(pair of socks), and 2 shoes(pair of…

Q: You have 200 different-looking tiles. (Each is a different solid color. You only have one tile of…

A: Each tray will have 5 different tiles. First tray will have 5 different tiles out of 200 choices of…

Q: 3. In how many ways can you arrange 5 books on a shelf from available 10?

A: The number of all combination of n things, taken r at  time is given by:

Q: In a club with 5 male and 9 female members, how many 5-member committees can be chosen that have at…

A: We have to find no. If ways to arrange.

Q: 6. A bin of golf tees has 7 different colors. You reach in and grab 100 tees. How many different…

A:

Q: A 6-digit phone number cannot start with 0 or 1. Assume that there are no restrictions on the…

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Q: If 4 marbles are pulled from the bucket, determine the number of different 4-sets of marbles that…

A: There are 13 marbles which contains 8 red ad 5 blue marbles. (i)When 4 marbles are pulled, where 2…

Q: 10. How many ways can 10 people line up if Carly and David must be next to each other?

A: Step 1:   Step 2: Step 3: Step 4:

Q: A student is to answer 7 out of 10 questions in an examination. How many choices has she? How many…

A: The total number of questions: The number of questions she wants to answer:

Q: 5. How many arrangements can be made from 4 boys and 4 girls if they have to sit in a roundtable and…

A: We have given that  Number of boys=4 Number of girls=4

Q: 19.In how many ways can 4 girls and 3 boys be arranged around a camp fire if the 4 girls must be…

A:

Q: 8. Suppose Jack has 1 red ball, 1 orange ball, 1 blue ball, 1 yellow ball, 1 black ball and 1 green…

A: Given that  Jack has  Red ball = 1 Orange ball = 1 Blue ball  = 1 yellow ball = 1 black ball = 1…

Q: In how many ways can you seat two children and three adults in a row of five seats if the children…

A: Number of ways of arranging two children       =2! Number of ways of arranging three adults…

Q: 10. Suppose that 5 teachers and 8 students volunteered to be on a graduation committee. The…

A: Given that  Teachers = 5 , Students = 8 Committee consists 2 teachers and 3 students  Note : nCr =…

Q: 2. Babui has 5 roses of each of the colors red, yellow, blue, and black (total 20 roses). In how…

A: Introduction: A combination may be a mathematical technique for crucial the quantity of potential…

Q: How many formations of committee from 10 persons are possible if the committee consists of one…

A: In this question, the concept of Permutation and Combination is applied. Permutation  Permutations…

Q: 8. In how many ways can 4 girls and 5 boys sit in a row if the boys and girls must alternate?

A: (8) Number of girls = 4 Number of boys = 5 The arrangement of boys and girls must sit alternate in a…

Q: In how many ways can a bag of three identical balls and four identical coins be formed from a group…

A: Given: Total number balls =12 Total number coins =12

Q: An urn contains 8 red balls, 3 green balls, and 1 white ball. Three are drawn simultaneously. Answer…

A: Given information: Number of red balls, r = 8 Number of green balls, g = 3 Number of white balls, w…

Q: Dennis and Grace got married today and are having a photo session together. At a photo session…

A: Given information: There are 12 men and 10 woman taking the photo. Dennis doesn't want any men in…