7. How many ways are there that in a class of 60 students, 2 students will not have the same birth date?

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: In how many ways can 6 girls and 3 boys sit on a row of 9 chairs in such a way that no two boys sit…

A: we have to solve given problems:

Q: An insurance agent has a list of 7 prospects and decides to telephone 5 of the prospects today and…

A: we want to find different ways can the agent telephone the prospects

Q: How many ways are there to arrange 12 identical apples and five different oranges in a row so that…

A: Here, arrange 12 identical apples and five different oranges in a row so that no two oranges will…

Q: In how many ways can one put 8 adults and 4 children in a row, such that no two children are next to…

A: We have given that there are 8 adults and 4 children in a row. Here our claim to to show in how many…

Q: 3) In how many ways can three bracelets be selected from a box of ten bracelets?

A:

Q: In how many ways can you distribute n pennies to k children if each child is supposed to get at…

A:

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

A:

Q: How many different ways can a club of 20 members select a 3-member officer-nominating committee from…

A: Given Information:  Total members = 20  Number of members to be selected = 3

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: Three cards are chosen without replacement from a deck of 52 cards and placed in order from first to…

A: In the deck of 52 cards, there are total 4 6's. (One for each of hearts, diamonds, spades and clubs)…

Q: In how many ways can we seat 6 boys and 3 girls on a row of seats so that no two girls sit next to…

A: If no two girls can sit together, then we need to alternate boy and girl. We can start with a boy…

Q: How many possible ways can the top 5 finishers come in during a race with 24 racers? Each place…

A: This is a permutation problem.   Out of the 24, there will be 5 racers in the top 5.

Q: In how many ways can first and second prize be awarded in contest with 100 people, assuming that…

A: There are 100 students in the contest.

Q: 2. Suppose there is a race between 9 friends. How many ways can the race be completed if John is…

A: Here use concept of total arrangement

Q: How many ways are there to arrange 6 different unique chairs (i.e., each chair is different from any…

A: Explanation of the answer is as follows