1. Evaluate the given expression. P(7, 7)

2. Evaluate the given expression. P(8, 6)

3. Evaluate the given expression. C(6, 3)

4. Evaluate the given expression. C(n, n 2)

5. In how many ways can six people line up at a checkout counter in a supermarket?

6. In how many ways can an investor select three mutual funds for his investment portfolio from a recommended list of nine mutual funds?

7. Find the number of distinguishable permutations that can be formed from the letters of the word MILLENNIALS.

8. How many different signals can be made by hoisting two yellow flags, two green flags, and three red flags on a ship's mast at the same time?

9. A student is given a reading list of eight books from which he must select four for an outside reading requirement. In how many ways can he make his selections?

10. Seven people arrive at the ticket counter of Starlite Cinema at the same time. In how many ways can they line up to purchase their tickets?

11. L.A. Wedding Caterers offers a wedding reception buffet. Suppose a menu is planned around five different salads, six entrees, five side dishes, and eight desserts. There are eight different choices of salads, ten different choices of entrees, eight different choices of side dishes, and ten different choices of desserts. How many menus are possible?

12. C & J Realty has received 16 inquiries from prospective home buyers. In how many ways can the inquiries be directed to any two of the firm's real estate agents if each agent handles eight inquiries?

13. A student taking an examination is required to answer exactly 10 out of 15 questions.

(a) In how many ways can the 10 questions be selected? (b) In how many ways can the 10 questions be selected if exactly4of the first5questions must be answered?

14. JCL Computers has five vacancies in its executive trainee program. In how many ways can the company select five trainees from a group of fifteen female and fifteen male applicants if the vacancies

(a) Can be filled by any combination of men and women? (b) Must be filled by two men and three women? 15. Twelve graduate students have applied for three available teaching assistantships. In how many ways can these assistantships be awarded among the applicants if

(a) No preference is given to any one student? (b) One particular student must be awarded an assistantship? (c) The group of applicants includes seven men and five women and it is stipulated that at least one woman must be awarded an assistantship?