A class has 30 students enrolled. In how many ways can: a four be put in a row for a picture? This is the number of 4-permutations from a set of 30, which is P 30, 4. A class has 20 women and 16 men.

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A class has 30 students enrolled. In how many ways can: a four be put in a row for a picture? This is the number of 4-permutations from a set of 30, which is P 30, 4. A class has 20 women and 16 men. In how many ways can you a put all the students in a row? Solution: a There are 36 students. They can be put in a row in 36! By the product rule, this can be done in 20!

A certain type of push-button door lock requires you to enter a code before the lock will open. Several states play a lottery game called Mega Millions. Solution: The number of ways to choose three women is C 10, 3 and the number of ways to choose two men is C 7, 2. Solution: Note that there are 10 odd integers and 9 even integers in S. Solution: Visualize a row of ten blanks. Here is one way to solve the problem. Here is a second way to approach the problem.

These ten letters can be arranged in 10! Here is a third way to approach the problem. Find the number of ways to take an ordinary deck of 52 playing cards and break it into: a four equal piles, labeled A, B, C, D.

Hence the answer is the answer to part a divided by 4! Solution: There are 13 odd numbers; we can choose two in C 13, 2 ways. Solution: b The prime numbers in S are 2, 3, 5, 7, 11, 13, 17, 19, and 23, and there are C 9, 3 ways to select three of them.

Solution: There are very few subsets with this property. Thus, there are four such subsets.

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## Discrete Mathematics

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