This is a combinatorics question.

Consider alphabet S = {a, b, c, d}.

(a)How many words of length n over alphabet S are there? Give the simplest answer. Explain.

(b)How many words of length n over alphabet S contain exactly two distinct letters? Give the simplest answer. Explain.

(c)How many words of length 15 contain 5 as, 2 bs, 4 cs and 4 ds? Give the simplest answer. Explain.

(d)In how many words of length 15 over alphabet S one letter occurs 5 times, another letter occurs 2 times, and the remaining two letters occur 4 times each? Give the simplest answer. Explain.