1. Warm Up 2/1/11 1.What is the probability of drawing three queens in a row without replacement? (Set up only) 2.How many 3 letter permutations can be made from the letters in the word ORANGE? __ ___ ___ 3. Evaluate

2. 1) 30 2) 48 3) 120 4) 24 5) 30 6) 120 7) 6 8) 42 HW answers 9) 10·9·8·7·6·5 10) 8·7·6·5·4 11) 9·8·7·6 12) 24 13) 256 14) 60 15) 125 16) 30 17) 36 18) 5·4·3· 4·3·2·1 19) 5·5·5· 4·4·4·4 20) 3·2·1· 4·3 21) 3·3·3· 4·4 22) 12 23) 30 24) 120 25) 420 26) 3360

3. 15.3 COMBINATIONS OBJECTIVE: To find the possible number of arrangements using COMBINATIONS

4. Permutation: Order matters (phone #, password, etc) Combination: Order DOES NOT matter (dealing cards, teams, etc) Combination formula:

5. Example 1: How many 4-person teams can be formed from a group of 7 people?

6. 2. How many 5-letter combinations can be made using the letters A, B, C, D, E? Their order is not important.

7. Practice 1) 2)3) 4)

8. Combinations Using Pascal’s Triangle 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1 1 8 28 56 70 56 28 8 1 0 th row 1 st row 2 nd row 3 rd row 0 th term 1 st term = 6 th row, 2 nd term = 15 = 5 th row, 5 th term = 1

9. Practice- Use Pascal’s Triangle 1) 2)3)