# 12 math

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there are 8 opposite sex married couples at a party. two people are chosen at random to win a door prize.
A. what is the probability that the 2 people will be married to each other?
B. what is the probability that the 2 people will be same sex?
C. if 6 people are chosen whats the probability that they are 3 married couples?

• 12 math -

a) the number of ways to choose 2 out of the 16 people is C16,2) = 120
there are 8 couples married to each other, so the prob is 8/120 = 1/15

b) the number of ways that the two chosen are different is C(8,1)xC(8,1) = 64
so the number of ways that they are the same is 120-64 = 56
so prob they are the same sex = 56/120 = 7/15

Now you try c) and explain your reasoning to us

("opposite sex married couples", wouldn't Sarah Palin be proud of that textbook author, lol)

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