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

A 32

B 48

C 64

D 96

Correct Answer: Option C

We may have (1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).

Required number of ways = (3C1 x 6C2) + (3C2 x 6C1) + (3C3)

= {3 x (6 x 5)/( 2 x 1)} + [{(3 x 2)/( 2 x 1)} x 6] + 1

= (45 + 18 + 1)

= 64.