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?

48
64
63
45

Correct Answer: 64

Explanation:

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

Required number of ways= $3 C 1 * 6 C 2 + 3 C 2 * 6 C 1 + 3 C 3$ = (45 + 18 + 1) =64

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