1. Use Combinations and the Binomial Theorem
Section 10.2

2. Objectives:
Use combinations
Apply the binomial theorem

3. Key Vocabulary:
Combination
Pascal’s triangle
Binomial theorem

4. Combinations

5. Example 1:
A standard deck of 52 playing cards has 4 suits with 13 different cards in each suit.
If the order in which the cards are dealt in not important, how many different 5-card hands are possible?
In how many 5-card hand are all 5 cards of the same color?

6. Example 2:
William Shakespeare wrote 38 plays that can be divided into three genres. Of the 38 plays, 18 are comedies, 10 are histories, and 10 are tragedies.
How many different sets of exactly 2 comedies and 1 tragedy can you read?
How many different sets of at most 3 plays can you read?

7. Example 3:
During the school year, the girl’s basketball team is scheduled to play 12 home games. You want to attend at least 3 of the games. How many different combinations of games can you attend?

8. #1: Find the number of combinations.

9. #2: Find the number of combinations.

10. #3: Find the number of combinations.

11. #4: Find the number of combinations.

12. Pascal’s Triangle

13. Example 4:
The 6 members of a Model UN club must choose 2 representatives to attend a state convention. Use Pascal’s triangle to find the number of combinations of 2 members that can be chosen as representatives.

14. #6: Complete.
In Example 4, use Pascal’s triangle to find the number of combinations of 2 members that can be chosen if the Model UN club has 7 members.

15. Binomial Theorem

16. Example 5:
Use the binomial theorem to write the binomial expansion.

17. Example 6:
Use the binomial theorem to write the binomial expansion.

18. #7: Use the binomial theorem to write the binomial expansion.

19. #8: Use the binomial theorem to write the binomial expansion.

20. #9: Use the binomial theorem to write the binomial expansion.

21. #10: Use the binomial theorem to write the binomial expansion.

22. Example 7:
Find the coefficient of x4 in the expansion of

23. #11: Find the coefficient of the term in the expansion.

24. #12: Find the coefficient of the term in the expansion.

25. Homework Assignment
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