Question:

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?

My answer: n(S) = (16 2) n(E) = ( 8 1)

P(married couple chosen) = (8 1) ÷ (16 2) = 8/20 = 1/15

Therefore, the probability is 1/15.

c) If 6 people are chosen, what is the probability that they are 3 married couples?

My answer: n(S) = (16 6)

n (E) = (8 3)

Therefore, P(3 married couples chosen) = (8 3)÷ (16 6) = 56/8008 = 7/1001

Thus, the probability that the 6 people chosen will be 3 married couples is 7/1001.

Please check for me and advise! THANK YOU