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

There are 2 white, three black and four red balls.
We have to draw 3 balls, out of these 9 balls in which atleast one black ball is included.
Hence, we can select the balls in the following ways.
`{:("Black balls", 1, 2, 3),("Other than black", 2, 1, 0):}`
`therefore` Required number of selections `= ""^(3)C_(1) xx ""^(6)C_(2) + ""^(3)C_(2) xx ""^(6)C_(1) + ""^(3)C_(3) xx ""^(6)C_(0)`
`= 3 xx 15 + 3 xx 6 + 1`
`=45 + 18 + 1 = 64`