Q. 205.0( 1 Vote )
A committee of 3 persons is to be constituted from a group of 2 men and 3 women. In how many ways can this be done? How many of this committee would consist of 1 man and 2 women?
Answer :
Given that we need to select 3 persons out of 2 men and 3 women,
Let us assume the no. of ways of selecting be N,
⇒ N = selecting 3 persons out of total 5 persons
⇒ N = 5C3
We know that 
And also n! = (n)(n – 1)(n – 2)…………2.1
⇒ 
⇒ 
⇒ 
⇒ N = 10 ways
The no. of ways of selecting 3 persons out of 2 men and 3 women is 10.
(ii) It is told that 1 man and 2 women should be selected out of 2 men and 3 women.
Let us assume the no. of ways of selection be N1,
⇒ N1 = (selecting one man out of 2 men) × (selecting 2 women out of 3 women)
⇒ N1 = (2C1) × (3C2)
We know that 
And also n! = (n)(n – 1)(n – 2)…………2.1
⇒ 
⇒ 
⇒ 
⇒ N1 = 6 ways
The no. of ways of selecting 1 man and 2 women is 6.
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