# Permutaion and Combination

1. A group of 3 students is to be selected from a group of 12 students to take part in a class in cell biology.

a. In how many ways can this be done?

b. In how many ways can the group who will not take part will be chosen?

2. After studying all night for a final exam, a bleary eyed student randomly grabs 2 socks from a drawer containing 9 black, 6 brown, and 2 blue socks all mixed together. What is the probability that she grabs a matched pair?

3. Argue that the probability that in a group of n people exactly one pair have the same birthday is

(n/2). (p(365,n-1)/365 ^n)

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#### Solution Preview

1. a. 12C3=12*11*10/(1*2*3)=220

b. 12C9=12*11*10/(1*2*3)=220

2. She can pick any of the first socks, but the second one should match the first one, so the probability will be

P(matched pair) = P(first one is black)*P(second one is black/first one is ...

#### Solution Summary

This solution contains over 100 words and calculations to aid you in understanding the solution to these questions.