# Permutations of a sequence of words

I've been given a question in class and I just wanted to confirm the answer

1) How many 3 letter sequences are possible that use the letters m, a, t, h, s at most once each?


For this question I know to use permutations as the order is sensitive as we are dealing with sequences so I did this: 3! or P(3,3) andre of my got 6.

The condition that states "at most once each" is throwing me off a bit and I am unsure of my answer.

So is this correct? if not how would I solve this question?

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5 choices for the first letter, 4 for the second, 3 for the third... so? – DavidP Mar 27 '14 at 23:34
"At most once each" means "use one or none", that is: "select without repetition". – Graham Kemp Mar 27 '14 at 23:38

$\mathrm{P}(\mathbf{3},3)$ or $\,^\mathbf{3}\mathrm{P}_3$ means: Count the distinct ordered sequences by selecting without repetition 3 symbols from a set of 3 distinct symbols. That is $\frac{\mathbf{3}!}{(\mathbf{3}-3)!}$