Question

A committee of five people is to be chosen from four married couples. a) How many different committees are there? b) What is the probability that a committee consists of three women and two man ? (4) 1. c) What is the probability that a committee has exactly one of married couples? d) What is the probability that a committee has at least one of married couples?

Answer 1

a)

number of committee =N(selecting 5 from 8 people)=⁸C₅ =8!/(5!*(8-5)!)=56

b)

P(3 women and 2men) =P(selecing 3 women from 4 and 2 men from 4)=⁴C₃ *⁴C₂ =4*6 =24

c)

P(exactly one married couple)=P(select one married couple from 4 and then have 1 choice from each of remaining couples)=⁴C₁*2*2*2/56 =32/56=4/7

d)

P(at least one married couple)=1 (As there are 4 couples and 5 people need to be selected therefore one married couple needs to be there)