A box contains 2 white balls, 3 black balls & 4 red balls. In how many ways can three balls be drawn from the box if atleast one black ball is to be included in draw (the balls of the same colour are different).

Options

A. 84
B. 20
C. 64
D. 104

Answer

C

Explanation

There are 9 balls in the box out of which three balls can be draw in `""^(9)C_(3)` ways. But there ways also include those ways in which no black balls is drawn. The total number of such ways is `""^(6)C_(3)`.
`:.` Number of ways in which at least one black ball is included = Total number of ways of drawing 3 balls from 9 balls - Number of ways of drawing no black ball from 9 balls `""^(9)C_(3)-""^(6)C_(3)=84-64`.