Question

Use exponential generating functions to determine the number of strings of length 12 with the following properties:

1) Each string is made up of the characters ”a”, ”b”, ”c”, ”d” (some characters may not appear at all).

2) The number of times that ”a” appears is even, and the number oftimes that ”b” appears is odd.

Find a closed-form formula for the exact answer – e.g. I’m looking foran answer like 5n+ 2n, not∑ni=12n(3ni).

Answer 1