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

Philoid · Accepted Answer

Given that we need to find no. of ways of selecting 5 persons out of 6 men and 4 women in which at least one woman is necessary.

Let us assume the no. of ways of selection be N.

⇒ N = (total no. of ways of selecting 5 persons out of all 10 persons) – (No. of ways of selecting 5 persons without any women)

⇒ N = (¹⁰C₅) – (⁶C₅)

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒ N = 252 – 6

⇒ N = 246

∴ The total no. of choosing 5 persons with at least one woman is 246.