1. Pennant Fever Review Adam Johnson Nate Levin Ian Olsen

2. Unit Problem  The good guys and the bad guys each have 7 games to play. Based on each of their winning records (.62 good guys and.6 bad guys) we must determine the chances each team has to win the pennant.

3. Key Topics  Combinations  Permutations  Pascal’s Triangle  Factorials  Binomial Theorem

4. Factorials  Multiplication pattern  Sign is “!”  Multiply the coefficient of “!” by every whole number below it, excluding numbers zero and below.  4!=4*3*2*1=24

5. Combinations  nCr  n!/(n-r)!*r!  Order doesn’t matter  Bowls of ice cream  Answer question #1 on worksheet now

6. Question #1  12C1 x 7C1 x 4C1 x 5C1=?  12x7x4x5=1680  When r value is equal to one, the final answer of the value is equal to the n value  (12!/(12-1)!*1!)*(7!/(7-1)!*1!)*etc…  5C1=5  5*4*3*2*1=120  120/4!=5

7. Permutations  nPr  n!/(n-r)!  Order does matter  Cones of ice cream  Answer question #4 on worksheet now

8. Question #4  22P7=?  22!/(22-7)!=859,541,760  22!=1.12E21  Answer question #2

9. Question #2  Explain the difference between 10P7 and 10C7  Well P will obviously be larger as the order of the combinations matter, increasing the total number of possibilities.

11. Question #2 (Continued)  We can see the steps that are different in the previous slide that make 10P7 and 10C7 different.  Due to the difference in order mattering or not, the final answer will change drastically.

12. Pascal’s Triangle  Shows the binomial coefficient  Shows nCr values

13. Binomial Theorem  Finds the coefficients of binomial  Answer question #8

14. Question #8  (2X+3)^5