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Question
A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box, if atleast one black ball is to be included in the draw
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Solution
We have 2 white, 3 black and 4 red balls in a box.
3 balls are to be drawn out of 9 balls atleast one black ball is to be included
So, the possible selection is (1 black and 2 other balls)
or (2 black and 1 other ball)
or (3 black and no other ball)
So, the number of possible selection is
= 3C1 × 6C2 + 3C2 × 6C1 + 3C3 × 6C10
= 3 × 15 + 3 ×6 + 1 × 1
= 45 + 18 + 1
= 64
Hence, the required selection = 64.
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