MTH 376 Discrete Mathematics Name Exam 1 Ch 1 to 3 Bruald

MTH 376 – Discrete Mathematics Name:____________________ Exam 1 – Ch 1 to 3 – Brualdi

3. A football team of 11 players is to be selected from a set of 15 players, 5 of whom can play only in the backfield, 8 of whom can play only on the line, and 2 of whom can play either in the backfield or on the line. Assuming a football team has 7 men on the line and 4 men in the backfield, determine the number of football teams possible.   
4. At a party there are 15 men and 20 women.

(a) How many ways are there to form 15 couples consisting of one man and one woman?

(b) How many ways are there to form 10 couples consisting of one man and one woman?

5. Use the word ADDRESSES for the following:

a. How many total permutations are there of the letters of the word ADDRESSES?

b. How many 8permutations are there of these nine letters?

c. How many 8permutations are there of these nine letters in a circular fashion?

6. Determine the number of 11permutations of the multiset S = {3 a, 3 b, 3 c, 3 d}.   

7. A bagel store sells six different kinds of bagels. Suppose you choose 15 bagels at random. What is the probability that your choice contains at least one bagel of each kind?

8. A bag contains 100 apples, 100 bananas, 100 oranges, and 100 pears. If I pick one piece of fruit out of the bag every minute, how long will it be before I am assured of having picked at least a dozen pieces of fruit of the same kind?

9. There are 250 students living a dorm. Can we be assured/guaranteed that there are 5 students who share a birthday in the same month? How do you know?   

Solution