Answer to Question #56773 in Combinatorics | Number Theory for Gabzmann

Question

How many words can we build using exactly 5 A's, 5 B's and 5 C's if the first 5 letters cannot be A's, the second 5 letters cannot be B's and the third 5 letters cannot be C's? Hint: Group the different ways according to the number of B's in the first group.