Combinations Accelerated Math II November 17, 2014.

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Presentation transcript:

Combinations Accelerated Math II November 17, 2014

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 =

= ? 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 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?

= 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!

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

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

= 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

= 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) =

= 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

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

= 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)

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 #

Assignment Page 647: 1-9 all, odd, all Good luck!