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?

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

Required number of ways= $3C1*6C2+3C2*6C1+3C3$ = (45 + 18 + 1) =64