In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
Question:
In how many ways can a committee of 5 persons be formed out of 6 men and 4 women when at least one woman has to be necessarily selected?
Solution:
5 persons are to be selected out of 6 men and 4 women. At least, one woman has to be selected in all cases.
Required number of ways $={ }^{4} C_{1} \times{ }^{6} C_{4}+{ }^{4} C_{2} \times{ }^{6} C_{3}+{ }^{4} C_{3} \times{ }^{6} C_{2}+{ }^{4} C_{4} \times{ }^{6} C_{1}$
$=60+120+60+6$
$=246$