[64] A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn f

For Competitive Exams

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?

Explanation:

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 \times 5 $ \dfrac{6 \times 5}{2 \times 1} $)]$ + $ [(\dfrac{3 \times 2}{2 \times 1} \times 6]$ + 1
	= (45 + 18 + 1)
	= 64.

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