Question

A committee of $3$ women and $2$ men is to be formed from a pool of $11$ women and $7$ men. Calculate the total number of ways in which the committee can be formed.

• A. $3,465$
• B. $6,930$
• C. $10,395$
• D. $20,790$
• E. $41,580$

Answer 1

The correct option is A $3,465$

Number of ways of selecting $3$ women from $11$ women is ${{}^{11}C}_3=165$.

Number of ways of selecting $2$ men from $7$ men is ${{}^{7}C}_2=21$.

Total number of ways of selecting $3$ women and $2$ men is $145\times 21=3465$.