Download multinomial and the probability of getting the right letters in the right

Suppose we pick ten letters from an infinite pile of scrabble tiles, and arrange
them face down. What's the probability that they spell STATISTICS?
is the probability of getting the right letters in the right order.
Think of it in 2 steps. First, you need the right number of each letter. This is the
multinomial probability:
is the probability of getting the right number of each letter.
The probability of getting the order of the letters right, given the right number of
each letter, is the proportion of permutations which are correct:
This makes sense, because
n!
is the total number of permutations of the n slots, and
is the number of permutations that match the word STATISTICS.
If the word had unique letters only, this would be only 1 permutation.
If the word had just one letter repeated, it would be all n! permutations.