Question

A committee of 3 members is to be formed out of 3 men and 4 women. In how many different ways can it be done so that atleast one member is woman?

• A. 34
• B. 12
• C. 30
• D. 36
• E. None of these

Answer 1

The correct option is A 34

The committee can be formed in the following ways
(i) By selecting 2 men and 1 woman
(ii) By selecting 1 man and 2 women
(iii) By selecting 3 women
$\therefore$ Total number of ways of forming the committee
$={}^3{C}_2\times {}^4{C}_1+{}^3{C}_1\times {}^4{C}_2+{}^4{C}_3=3\times 4+3\times 6+4$
= 12 + 18 + 4= 34