# In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?

Question:

In how many ways can a committee of 5 be made out of 6 men and 4 women containing at least one women?

(a) 246

(b) 222

(c) 186

(d) none of these

Solution:

(a) 246

Required number of ways $={ }^{4} C_{1} \times{ }^{6} C_{4}+{ }^{4} C_{2} \times{ }^{6} C_{3}+{ }^{4} C_{3} \times{ }^{6} C_{2}+{ }^{4} C_{4} \times{ }^{6} C_{1}$

$=60+120+60+6$

= 246