In how many ways can a committee be formed of 5 members from 6 men and 4 women if committee has at l

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6.Permutation and Combination

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In how many ways can a committee be formed of $5$ members from $6$ men and $4$ women if the committee has at least one woman

A

$186$

B

$246$

C

$252$

D

None of these

(IIT-1968)

Solution

(b) The number of ways can be deduce as follows :

$1$ woman and $4$ men ${ = ^4}{C_1}{ \times ^6}{C_4} = 60$

$2$ women and $3$ men ${ = ^4}{C_2}{ \times ^6}{C_3} = 120$

$3$ women and $2$ men ${ = ^4}{C_3}{ \times ^6}{C_2} = 60$

$4$ women and $1$ man ${ = ^4}{C_4}{ \times ^6}{C_1} = 6$

Required number of ways $=60+120+60+6=246$.

Standard 11

Mathematics

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