Number of ways in which a committee of 6 members can be formed from 8 gentlemen and 4 ladies so that

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6.Permutation and Combination

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The number of ways in which a committee of $6$ members can be formed from $8 $ gentlemen and $4$ ladies so that the committee contains at least $3$ ladies is

A

$252$

B

$672$

C

$444$

D

$420$

Solution

(a) There can be two types of committees

$(i)$ Containing $3$ men and $3$ ladies

$(ii)$ Containing $2$ men and $4$ ladies

Required number of ways= ${(^8}{C_3}\, \times {\,^4}{C_3})\, + \,{(^8}{C_2}\, \times {\,^4}{C_4}) = 252$.

Standard 11

Mathematics

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