Question
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?
Answer: Option C
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We may have(1 black and 2 non-black) or (2 black and 1 non-black) or (3 black).
= (3C1 x 6C2) + (3C2 x 6C1) + (3C3)
\(\left(3\times\frac{6\times5}{2\times1}\right)+\left(\frac{3\times2}{2\times1}\times6\right)+1\)
= (45 + 18 + 1)
= 64.
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