Question

In a group of 18 boys and 22 girls, three people are chosen at random. What are the odds that 1 girl and 2 boys are selected?

Answer 1

Number of ways in which r items can be selected from n, nCr = n!/(r! x (n-r)!)

P(1 girl and 2 boys are selected) = Number of ways to select 1 girl from 22 x Number of ways to select 2 boys from 18 / Number of ways to select 3 people from total 40

= 22C1 x 18C2 / 40C3

= 22 x 153 / 9880

= 1683/4940

P(selection is not of 1 girl and 2 boys) = 1 - 1683/4940

= 3257/4940

Odds that 1 girl and 2 boys are selected = P(1 girl and 2 boys are selected) : P(selection is not of 1 girl and 2 boys)

= 1683/4940 : 3257/4940

= 1683 : 3257

= 1 : 1.935