Question

A committee of $3$ persons is to be constituted from a group of $2$ men and $3$ women.i) In how many ways can this be done? ii)How many of these committees would consist of $1$ man and $2$ women?

• A. $i)6$ $ii)10$
• B. $i)12$ $ii)10$
• C. $i)6$ $ii)16$
• D. $i)10$ $ii)6$

Answer 1

The correct option is D $i)10$ $ii)6$

(i) Total number of Candidates = 2 Men + 3 Women = 5

Person required in commitee = 3

No of ways = ${}^5{C}_3=10$

(ii) Total Men = 2

Total Women = 3

No of ways of selecting 1 man and 2 woman = ${}^2{C}_1{\times }^3{C}_2=2\ast 3=6$