A box contains 2 white balls, 3 black balls and 4 red balls. The number of ways three balls be drawn from the box, if atleast one black ball is to be included in the draw is …….. .

Explanation

Since, there are 2 white, 3 black and 4 red balls. It is given that atleast one black ball is to be included in the draw.
`therefore` Required number of ways `= ""^(3)C_(1) xx ""^(6)C_(2) + ""^(3)C_(2) xx ""^(6)C_(1) + ""^(3)C_(3)`
`= 3 xx 15 + 3 xx 6 + 1`
`= 45 + 18 + 1 = 64`