Problem Solving

Just need some help with this...

From a group of 3 boys and 3 girls, 4 children are to be randomly selected. What is the probability that equal numbers of boys and girls will be selected

A. 1/10
B. 4/9
C. 1/2
D. 3/5
E. 2/3

If the ans is D ie 3/5 then my explanation goes like this:-
Total no of events = Selecting 4 children from a group of 6
= 6C4 = 15
Favorable events will only be when 2 boys and two girls are selected (Since equal nos)
Selecting 2 Girls from a group of 3 Girls = 3C2 = 3
Selecting 2 Boys from a group of 4 Boys = 3C2 = 3
Total favorable events = 3x3 = 9
Prob = 9/15
or 3/5

Please correct if I am wrong

I agree with Vinay ans should be 3/5

Ok may be I am just getting very confused but here is what I did and I got the ans as 1/10

To get equal no of boys and girls u need to find the probability of selecting 2 girls and the probability of selecting 2 boys.

Probability of selecting a girl on the first chance is 3/6

and the prob of selecting a girl in the 2nd chance is 2/5

and the prob of selecting a boy in the 3rd round is 3/4

and the prob if selecting a boy in the 4th round is 2/3

So the prob of getting equal girls and boys is 3/6*2/5*3/4*2/3 = 1/10

Can some one pls tell me where I am going wrong???

thanks guys/gals the answer is 3/5. Really appreciate your taking the time.