Question

An unlimited number of red, white, blue and green balls are given. Ten balls are drawn. Find the number of ways of selection.

Answer 1

In this, the expression in x to be considered is 1 + x + x² + … to correspond to the unlimited number available in each colour. There are four such colours. The required number of ways is

Coefficient of x¹⁰ in [1 + x + x² + …]⁴ 

= Coefficient of x¹⁰ in (1/1 - x)⁴

= 11 x 12 x 13/6

= 286