From a group of 3 men and 4 women, a delegation of 2 is selected. let x be the random variable that represents the number of women selected. write the probability distribution and find the expected number of women in the delegation?

Let random variable x be the delegated number of men.
x values are 0, 1, 2, 3
The corresponding probabilities are:
P(x=0)=  3C2/7C2=3/21
P(X=1)=3C1*4C1/7C2=12/21
P(X=2)=3C2/7C2=3/21
P(X=3)=3C2/7C2=3/21

Hence the expected value will be:
E(x)=[0*3+1*12+2*3+3*3]/21
E(x)=27/21=1.29