10.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?
A. 48 B. 64
C. 69 D. 71
Answer:
we may have(1 black and 2 non-black) or ( 2 black and 1 non black) or ( 3 black).
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Required number of ways
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‹=›(3C1 × 6C2) + (3C2 ˜6C1) + (3C3)
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‹=›(3 x 6 x 5 / 2 x 1) + (3 x 2 / 2 x 1 x 6) + 1
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‹=› (45 + 18 + 1)
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= 64.
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