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6.Permutation and Combination
medium
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