Answer to Question #4582 in Statistics and Probability for KHALID JUTT

Question

From a group of 4 men and 5 women, how many committees of size 3 are possible (a) with no restrictions? (b) with 1
man and 2 women? (c) with 2 men and 1 woman if a certain man must be on the committee?

Answer 1

a) We choose 3 persons from 9, so there are 9!/(3!*(9-3)!) = 84 different committees.
b) We choose 1 man from 4 and 2 women from 5, so there are 4*5!/(2!*(5-2)!) = 40.
c) As a certain man is already chosen, we need to choose 1 man from 3 and 1 woman from 5, so 3*5 = 15.