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  • A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box , if at least one black ball is to be included in the draw.

A box contains two white, three black and four red balls. In how many ways can three balls be drawn from the box , if at least one black ball is to be included in the draw.
[Hint: Required number of ways ={ }^{3} \mathrm{C}_{1} \times{ }^{6} \mathrm{C}_{2}+{ }^{3} \mathrm{C}_{2} \mathrm{x}^{6} \mathrm{C}_{1}+{ }^{3} \mathrm{C}_{3}]

Answers (1)

Out of 2 white, 3 black and 4 red balls we have to draw 3 balls such that atleast one black is included.

The possibilities are:

a.1 black ball and 2 others b.2 black balls and 1 other (c)3 black balls

Number of selections = 3_{C_{1}} * 6_{C_{2}}+3_{C_{2}} * 6_{C_{1}}+3_{C_{3}} * 6_{C_{0}}

=3*15+3*6+1=45+18+1=64

Posted by

infoexpert21

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