Question

Prove that there will be only 24 selections containing at least one red ball out of a bag containing 4 red and 5 black balls. It being given that the balls of the same colour are identical.

Answer 1

There is no restriction about the number of balls (identical) to be drawn except that there will be at least one red ball. Hence we can have 1 or 2 or 3 or 4 red balls in the selection i.e. there are 4 ways of selection of red balls. For black balls there is no restriction. We may select 1 or 2 or 3 or 4 or 5 or no blackball i.e. there are 6 ways of selection of black balls Hence the total number of selection is 4 $\times$6 = 24.