MCQ - 148-8880

Correct Answer: C

Explanation:

This is possible when out of 4 members of the committee
(i) either all the four are men, or
(ii) 3 members are men and 1 member is a woman.
No. of selections in (i) = ⁵C⁴ = ⁵C¹ = 5
No. of selections in (ii) = ⁵C³ × ³C¹

$\genfrac{}{}{1px}{}{\mathrm{5\; \times \; 4}}{\mathrm{1\; \times \; 2}}$ × 3 = 30

total no. of selections = 5 + 30 = 35
Again, total number of equally likely cases
= ⁸C⁴
[Total no. of persons = 5 + 3 = 8]

=$\genfrac{}{}{1px}{}{\mathrm{8\; \times \; 7\; \times \; 6\; \times \; 5}}{\mathrm{1\; \times \; 2\; \times \; 3\; \times \; 4}}$ = 70

required probability = $\genfrac{}{}{1px}{}{35}{\mathrm{70}}$ = $\genfrac{}{}{1px}{}{1}{2}$