Although Rahul has solved this question.I solved in a direct way.

There are 5 dolls and 5 girls. 2 dolls are same.

One of the girls doesn't get a specific doll (G.I Joe doll).

Lets make 5 dashes _ _ _ _ _ (for 5 girls).

We fill the dash with the most restriction first.Since the smallest girl can't be alloted one of the dolls,she can only be alloted one of the 4 remaining dolls.

4 _ _ _ _

Now the second girl can be alloted any of the 4 remaining dolls [ one of the 5 dolls has already been alotted]

4 4 _ _ _

Similarly the third girl can be alloted any of the 3 reaming ones.

4 4 3 _ _

This is same procedure is repeated fot the 2 other girls

4 4 3 2 1.

Now don't forget that the question mentions that 2 of the dolls are identical. So divide by 2!.If 3 dolls were identical ,we would have divided by 3!.

(4*4*3*2*1)/2!=4*4*3=48.

This question was all about logic.I solved it 2 steps.