Q. 175.0( 1 Vote )
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?
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.
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