From 4 gentlemen and 6 ladies a committee of five is to be selected. The number of ways in which the committee can be formed so that gentlemen are in majority is -

Options

A. 66
B. 156
C. 4
D. none of these

Answer

A

Explanation

The committee will consist of 4 gentlemen and 1 lady or 3 gentlemen and 2 ladies
`therefore` the number of committees = ` ""^(4)C_(4) xx ""^(6)C_(1) + ""^(4)C_(3) xx ""^(6)C_(2) = 66`
Ans. [1]