1. Evaluate the following by showing at least one step with factorials.

a. 13C10

b. n!/(n-n-2)!(n-2)!

2. 2. Given S = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {2, 4, 6, 8, 10} and B = {5, 6, 7, 8, 9}, answer the following; a. A'

b. A n B

c. n(A u B)

d. (B n A')'

3. A pizza shop has 11 different toppings. a. In how many ways could you select toppings for a pizza? Assume you can not order a pizza with no toppings? b. In how many ways could you order a pizza with three toppings?

4.A three person committee is to be selected from 7 grade 11's and 9 grade 12's. In how many ways can a committee be selected if; a. With no restrictions? b. If the committee must have exactly 2 grade 12 students? c. If the committee must have at least one grade 12 student? d. If the committee must have at least one grade 11 and at least two grade 12's?

5. In how many ways can a swim team be chosen with a maximum of 4 people and a minimum of 1 person?

6. Expand and simplify the following binomial: (3^4 5)^4

7.Explain the difference between permutation and combination?

8.A fruit bowl contains the following fruits: 9 apples, 7 pears, 2 oranges, 4 plums, and 1 banana. a. How many ways can you reach into the fruit bowl and select at least one fruit? b. How many ways can you select fruit if you want to include at least one pear and no plums and bananas?

9. In poker, a hand of 5 cards is dealt from a standard deck of 52 cards. How many different possible 5 card hands consists of 2 pairs: 2 cards of one kind, 2 cards of another king and 1 cards completely different. (e. 2 Jacks, 2 Queens and 1 King)