1. Combinations Accelerated Math II November 17, 2014

2. Review Problem Suppose there are 21 members of Mu Alpha Theta. In how many different ways can we elect a Captain, a Co- Captain, a Secretary and a Treasurer from this group? Draw 4 blanks. 2120 19 18 = 143640

3. = ? New Idea... Suppose there are 21 people in Mu Alpha Theta. In how many different ways can we choose a team of 4 from this group? Draw 4 blanks. 2120 19 18 But wait! The order we picked you in doesn’t matter this time. A team of Riya, Anastasia, Radhesh and Yash is the same as a team of Yash, Riya, Radhesh and Anastasia. So what do we do?

4. = 5985 New Idea... Suppose there are 21 people in Mu Alpha Theta. In how many different ways can we choose a team of 4 from this group? Draw 4 blanks. Then divide by the number of ways we could arrange these four people! 2120 19 18 12 3 4

5. Combinations A combination is an arrangement of objects in which order is NOT important! Furthermore, the combination of n objects taken r at a time, written nCr or C(n, r) or is

6. Try These 5C35C3 5C25C2 7C07C0 7C77C7 = 10 = 1 6C56C5 8C48C4 6C16C1 = 6 = 70

7. = 84 Sample Problem #1 In how many different ways can I select 3 out of the 9 pumpkins left at Kroger to buy today? Draw 3 blanks. Then divide by the number of ways we could arrange these 3 pumpkins. 98 7 12 3

8. = 210 Sample Problem #2 There are 3 ghosts and 7 zombies at a Halloween party. In how many different ways can 4 of them be chosen to scare the other guests? C(10, 4) = 109 8 7 12 3 4

9. = 105 Sample Problem #3 There are 3 ghosts and 7 zombies at a Halloween party. In how many different ways can 4 of them be chosen to scare new guests if exactly 1 is a ghost? Move the ghosts to one room and the zombies to another... 3 1 7 6 5 1 2 3

10. Sample Problem #4 There are 3 ghosts and 7 zombies at a Halloween party. If we select 4 of them chosen at random to scare others, what is the probability that exactly two are ghosts? Remember the definition of probability… The sample space is C(10, 4) = 210

11. = 63 Sample Problem #4 There are 3 ghosts and 7 zombies at a Halloween party.. If we select 4 of them chosen at random to scare others, what is the probability that exactly two are ghosts? And the numerator is: C(3, 2)·C(7, 2) 32 12 7 6 12

12. There are 3 ghosts and 7 zombies at a Halloween party. If we select 4 of them chosen at random to scare others, what is the probability that exactly two are ghosts? So the probability is: = Sample Problem #4 210 63 3 10

13. Assignment Page 647: 1-9 all, 17-33 odd, 34-43 all Good luck!