Question

From a group of $4$ men and $4$ women, $5$ persons have to selected in which at least one man and one woman have to be included. In how many ways can it be done?

• A. $320$
• B. $640$
• C. $225$
• D. $56$

Answer 1

Answer: (D)

$56$

One man and one woman has to be there.

$1$ men and $4$ woman

$2$ men and $4$ woman

$3$ men and $1$ woman

$4$ men and $1$ woman

Number of ways ${=}^4{C}_1{\times }^4{C}_4$ +${}^4{C}_2{\times }^4{C}_3$ +${}^4{C}_3{\times }^4{C}_2$ +${}^4{C}_4{\times }^4{C}_1$$=56$