Math

MATH 182, MATHEMATICAL ANALYSIS II

Exam 2

1. Evaluate the following factorials, permutations, and combinations.

(a) 6! (b) (c)

(d) 6P4 (e) 5C2 (f) 7P5

2. The Postal Service is encouraging the use of 9-digit zip codes in most areas. How many zip codes are possible

(a) if only odd numbers can be used?

(b) the first number must be zero?

(c) the first number must be zero and the last number must be one?

3. How many different 8-letter radio station call letters can be made

(a) if the first letter must be W, and letters may be not repeated?

(b) if the first letter must be W, the fourth letter must be K, and letters may not be repeated?

(c) if repeats are allowed (but the first letter is W and the fourth letter is K)?

4. How many 5-member committees can be formed from a class consisting of 9 students? What if one of the students is to be designated the president, one is to be designated the vice-president, and one is to be designated secretary?

5. In a game of musical chairs, 10 children will sit in 8 chairs arranged in a row. Two children will be left out. In how many ways can the 10 children find seats?

6. A mailman has special delivery mail for 15 customers.

(a) In how many ways can he arrange his schedule to deliver to all 15?

(b) In how many ways can he schedule deliveries if he can deliver to only 8 of the 15?

7. Five orchids are to be selected from a collection of 12 for a flower show.

(a) In how many ways can this be done?

(b) In how many different ways can the group of 5 be selected if 2 particular orchids must be included?