Answer to Question #124334 in Statistics and Probability for Yasini

Question

A task force studying sex discrimination wishes to establish a subcommittee. If the subcommittee is to consist of 11 members chosen from a group of 23 men and 19 women, find the probability that the subcommittee consists of
(I)6 men and 5 women
(II)all women

Answer 1

Given :

Total members = 23+19=42

So there are 42C₁₁ = 4280561376 ways of selecting all 11 members .

Part a)

There are 23 C 6 = 100947 to pick 6 men (from a pool of 23 men)

There are 19 C 5 = 11628 ways to pick 5 women (from a pool of 19 women)

There are 100947*11628 = 1173811716

to pick a committee of 11 people where there are 6 men and 5 women.

Hence required probability = 1173811716/4280561376=0.274

Part b)

There are 19 C 11 = 75582 to pick a committee of all women.

Hence required probability =75582/4280561376 =0.0000176