Question

Out of 5 women and 4 men, a committee of three members is to be formed in such a way that atleast one member is a woman. In how many different ways can it be done?

• A. 80
• B. 84
• C. 76
• D. 96
• E. None of these

Answer 1

The correct option is A 80

The committee will be formed as follows
(i) 1 woman and 2 men
(ii) 2 women and 1 man
(iii) 3 women.
$\therefore$ Required number of committees
${=}^5{C}_1{\times }^4{C}_2{+}^5{C}_2{\times }^4{C}_1{+}^5{C}_3=5\times \frac{4\times 3}{1\times 2}+\frac{5\times 4}{1\times 2}\times 4+\frac{5\times 4\times 3}{1\times 2\times 3}$
= 30 + 40 + 10 = 80