Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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?

share|improve this question
    
5 choices for the first letter, 4 for the second, 3 for the third... so? –  David Peterson Mar 27 at 23:34
    
"At most once each" means "use one or none", that is: "select without repetition". –  Graham Kemp Mar 27 at 23:38

1 Answer 1

$\mathrm{P}(\mathbf{3},3)$ 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...

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.