this is my first post here

I'm studying for an exam and have problems with simplifying math problems including factorials.

Here is an example 1: $$ \frac{(n-3)!}{132} =10! \implies n=\ ? $$ apparently the answer is $15$ but i dunno the way?

another example 2: $$ \frac{(a-3)!}{x!} = 120 \implies \min(a+x)=\ ? $$ (answer is $8$)


closed as off-topic by user296602, Shailesh, Namaste, Did, user223391 Dec 28 '17 at 2:36

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    $\begingroup$ Welcome to MSE. Try using mathjax to make your question more presentable. $\endgroup$ – Mohammad Zuhair Khan Dec 27 '17 at 16:51
  • $\begingroup$ hi. thnax for your welcome and also i don't know what mathjax is and how to use it really 🤔 $\endgroup$ – Danial Nikpeyman Dec 27 '17 at 22:05

Note that $132=11\times12$. So\begin{align}\frac{(n-3)!}{132}=10!&\iff(n-3)!=12\times11\times10!=12!\\&\iff n-3=12\\&\iff n=15.\end{align}Can you do the other one?

  • $\begingroup$ wow! thak you so soo much. it looks so easy when u explained it! and i feel stupid for not being able to solve the other one! except for the part i could find 120=5! 😅 $\endgroup$ – Danial Nikpeyman Dec 27 '17 at 22:09
  • $\begingroup$ i got it! thank you so much again! $\endgroup$ – Danial Nikpeyman Dec 28 '17 at 10:04

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