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Six students in a math class all have to present their homework to their teacher, one student insists on being the first one to present. If the student's request is granted how many ways are there to schedule the presentation?

I tried $1 \times 5! = 120$. I don't know if it's the right answer.

N. F. Taussig
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    Please, even if you wouldn't ordinarily on the internet, observe the rules of grammar and reasonably polite communication on this site. (We get tons of questions, and lots of text-speak is annoying to deal with.) As for your question: How many ways can the teacher choose the second student? After she's picked that one, how many ways can she choose the third? – Chris Nov 16 '17 at 06:34
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    i tried 1x5! = 120 idk if its the right answer –  Nov 16 '17 at 06:35
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    That seems correct to me. – videlity Nov 16 '17 at 06:39

1 Answers1

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It is indeed permutation. It is $1 *$ $ _{(X-1)}$$P$$_5$, for X=amount of people in the class. The first one with the request is not counted (because he goes first. Period. We only have the schedule the remaining five), so that's why we only have to pick the remaining five, and have the choice of $X-1$ (We don't want the first one two times, right?). This should answer your question.

EDT: Yes, $1 * 5!$ is the right answer for $X = 6$ (which I think is the case, by re-reading your question), because $$_{6 - 1}P_5 = _5P_5 = \frac{5!}{(5-5)!} = \frac{5!}{0!} = \frac{5!}{1} = 5! = 120$$ So yeah, that's the right answer.

SuperSjoerdie
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  • I am a bit confused by your notation. What is $(X-1)P5$ meaning? – TomGrubb Nov 16 '17 at 06:59
  • It means $\frac{(X-1)!}{(X-1-5)!} = \frac{(X-1)!}{(X-6)!}$, so that from the remaining $X - 1$ people ($X - 1$, because one, the first one, has been picked already), we take 5 people (5, because one presentation has been held already). Does that make it more clear to you @ThomasGrubb ? – SuperSjoerdie Nov 16 '17 at 07:14
  • I just made a small change to the way I wrote the permutation, maybe that makes it a bit more clear too. – SuperSjoerdie Nov 16 '17 at 09:09