Question

Four persons are chosen at random from a group of 10 persons consisting of 4 men and 6
women. Three of the women are sisters. Calculate the probabilities that the four persons chosen
will
a) Consist of 4 women.
b) Consist of 2 women and 2 men
c) Include the three sisters
d) Do not include the three sisters.

Answer 1

a) prob(4 women)
= C(6,4)/C(10,4)
= 15/210
= 1/14

b) prob(2 women, 2 men)
= C(6,2)C(4,2)/C(10,4)
= 15(6)/210
= 3/7

c) with 3 sisters in, we need just one more of the remaining7 (could be man or woman)
prob(of event as stated)
= 1x C(7,1)/210
= 7/210 = 1/30

d)
prob(choosing any 4 of the remaining 7)
= C(7,4)/C(10,4)
= 35/210
= 1/6

Answer 2

Calculate the number of ways of selecting the four people if the are no restrictions