InterviewSolution
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InterviewSolution
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From 8 gentlemen and 5 ladies, a committee of 4 is to be formed. In how many ways can this be done. (a) when the committee consists of exactly three gentlemen? (b) when the committee consists of at most three gentlemen? |
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Answer» (a) We have to select three out of 8 gentlemen and one out of 5 ladies. Hence, the number of ways in which this can be done `=.^(8)C_(3)xx.^(5)C_(1)=280` (b) The committee is to contain at most three gentlemen, i.e., it may contain either 1,2 or 3 gentlemen. Hence, the total number of ways `=.^(8)C_(1)xx.^(5)C_(3)+.^(8)C_(2)xx.^(5)C_(2)+.^(8)C_(3)xx.^(5)C_(1)=80+280+280=640`. |
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