Question

Out of $2$ men and $3$ women a team of two persons is to be formed such that there is exactly one man and one woman. Write the sample space of this experiment, then the total no. of combinations of team possible are

• A. $9$
• B. $6$
• C. $4$
• D. $12$

Answer 1

Answer: (B)

$6$

Given,
A team contains 2men and 3 women.
But 2 persons have to be selected such that there is exactly 1 men and 1 women.
The no.of combinations${=}^2{C}_1{\ast }^3{C}_1=6$ (i.e., selecting 1 men out of 2 men=${}^2{C}_1$,selecting 1woment out of 3 women=${}^3{C}_1$)
Sample space={$M1W1,M1W2,M1W3,M2W1,M2W2,M2W3$}