Let $\displaystyle A = {a_1, a_2, . . . , a_k}$ be an alphabet, and let n_i denote the number of appearances of

letter a_i in a word. How many words of length n in the alphabet A are there for which

$\displaystyle k = 3, n = 10, n_1 = n_2 + n_3$ and $\displaystyle n_2$ is even?