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?
$\mathrm{P}(\mathbf{3},3)$ 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 $\frac{\mathbf{3}!}{(\mathbf{3}-3)!}$
However, you wish to do so from a set of 5, so...