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

There are 2 white, 3 black, and 4 red balls

Total Number of balls = 9

No of ways of selecting 3 balls $=9_{{\mathrm{C}}_3}$

 $=\frac{9\times 8\times 7}{1\times 2\times 3}=84$

No of ways of selecting 3 balls from

2 white, and 4 red balls $=6_{{\mathrm{C}}_3}$

 $=\frac{6\times 5\times 4}{1\times 2\times 3}=20$

Number of ways of selecting 3 balls so that at least one black ball is selected $=84-20=64$