Question

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

Answer 1

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 x6 x 5+3 x 2x 6+ 12 x 12 x 1= (45 + 18 + 1)= 64.

hope it helps