b) you neglect to count the various ways you can have 3 boys and 2 girls, think of a 5 digit binary string. There are more than one with 3 1's and 2 0's
c) did you mix up b and c? In this case there is only one string, if you order it by age, that matches the criterion, 11100, out of the 32 possible strings. So in this case the probability is just
If you think of this as a probability tree you are being forced down a single path through the tree in contrast with b.