A subword is a sequence of consecutive letters inside another word. For example, BA is a subword of BABA and of ABBA, but BB is only a subword of ABBA.

The number of ways to arrange the letters in a word of length n with distinct letters is n! = 1\times 2\times ...\times n. By convention, we write 0! = 1

More generally, suppose a word of length n is made up of letters from the set {L1, L2, ..., Lm}, with k_1 instances of letter L_1, and k2 instances of letter L2,..., and k_m instances of letter Lm.

Then the number of ways to arrange the letters in the word is n! / K_1! k_2! ... K_m!

How many arrangements of the word AAAABCCCDD contain the subword ACDA?