Advanced Algebra Name______________________

Combinations and Permutations Worksheet Date____________ Period_____

1. Describe the difference between a permutation and a combination.

2. Calculate the following. Use may use your calculator.

a. 3! b. 6! – 2! c. (8)(7!)

d. 4! + 5! e. ₅P₃ f. ₁₂P₁

g. ₈P₆ h. ₄₀C₃ i. ₁₅C₈

j. k. l.

3. How many ways can 3 red, 7 yellow, 4 blue and 5 green marbles be lined up in a row?

4. How many ways can 5 children be selected from 12 for show and tell, if the order they are selected determines who goes first, second, etc.?

5. How many ways can 4 friends line up for a photograph?

6. The U.S. Senate has 100 representatives. How many 5 person committees are possible?

7. The student council at a school has 14 members. Every member shakes hand with everyone else exactly one time. How many hand shakes occur?

8. There are 9 points on a circle. How many different pentagons can be inscribed in the circle using any five of the points?

9. Mary Jo is taking a test. She can select 7 of the 10 questions to answer. How many combinations of questions can she make?

10. A hand of 6 cards is dealt from a deck of 52 cards. What is the probability that the hand consists of three 5’s and three 7’s?

11. You draw 3 cards from a deck of 52 cards. Give the probability that all three cards are diamonds.

12. Pancho’s Pizza offers ten different pizza toppings. How many different ways can Roberta choose one, two or three toppings for her pizza?