Last digits of a number turned into base 4

[westin]

The elves can only have 1 or 2 gifts. Using stars and bars, I got n = 63 choose 24. How can I figure out the last consecutive digits that are 0 when n is expressed in base 4?

 

[blamocur]

Using stars and bars, I got n = 63 choose 24.

How did you get that?

Hint #1: what are the numbers of gifts each of the elves can receive?