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Question
From a group of 7 men and 6 women, 5 people are to be selected to form a committee so that at least 3 men are there in the committee. In how many ways can it be done?
Options
756
735
564
645
MCQ
Solution
756
Explanation:
`""^7C_3xx ""^6C_2+""^7C_4xx""^6C_1+""^7C_5xx""^6C_0`
=`""^7C_3xx""^6C_2+""^7C_3xx6+""^7C_2xx1`
=`(7xx6xx5)/(3xx2xx1)xx(6xx5)/(2xx1)+(7xx6xx5)/(3xx2xx1)xx6+ (7xx6)/(2xx1)`
= 525 + 210 + 21 = 756
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Permutation and Combination (Entrance Exam)
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