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A box contains two white balls, three ...

A box contains two white balls, three black balls and four 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 ?

Text Solution

Verified by Experts

The correct Answer is:
64
Case I When one black and two others balls are drawn. `rArr` Number of ways `= ""^(3)C_(1) * ""^(6)C_(2) = 45`
Case II When two black and one other balls are drawn
`rArr` Number of ways `=""^(3)C_(2)*""^(6)C_(1) = 18`
Case III When all three black balls are drawn
`rArr` Number of ways `= ""^(3)C_(3) = 1`
`therefore` Total number of ways `= 45 + 18 + 1 = 64`
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