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?

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

= (³C₁ x ⁶C₂) + (³C₂ x ⁶C₁) + (³C₃)

=	❨	3 x	6 x 5	❩	+	❨	3 x 2	x 6	❩	+ 1
			2 x 1				2 x 1

= (45 + 18 + 1)

= 64.

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