Question

How many different committees of $5$ can be formed from $6$ men and $4$ women on which exactly $3$ men and $2$ women serve?

• A. $6$
• B. $20$
• C. $60$
• D. $120$

Answer 1

The correct option is D $120$

$3$ men can be selected from $6$ men in ${}^6{C}_3$ ways
And $2$ women can be selected from $4$ women in ${}^4{C}_2$ ways,
Thus by multiplication principle.
number of ways of selection of $5$ people for the committee is ${=}^6{C}_3\times {}^4{C}_2=20\times 6=120$