Test by Bikram | General Aptitude | Test 2 | Question: 10

Question

From a group of $6$ men and $5$ women, $4$ persons are to be selected to form a committee such that at least $2$ men are in the committee. In how many ways it can be done?

• A. $150$
• B. $250$
• C. $265$
• D. $115$

Answer 1

Number of ways $ = $ Total $-$ not possible cases

Number of ways $ = \binom{11}{4} - \left[\binom{6}{0}\times\binom{5}{4} + \binom{6}{1}\binom{5}{3}\right]$

Number of ways $ = 330 - 65 = 265$

$$\textbf{(OR)}$$

$\text{Atleast '2' means 2 (or) more $(\geq 2)$.}$

Number of ways $ = \binom{6}{2} \times \binom{5}{2} + \binom{6}{3} \times \binom{5}{1} + \binom{6}{4} \times \binom{5}{0}  = 265$

So, the correct answer is $(C).$

Answer 2

6C2*5C2 +6C3*5C1+6C4*5C0...

after solving it we get 265