Could someone please explain this to me

Pojebany

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Hi, could someone please explain how this: [MATH]n!/2!(n-2)![/MATH] gets to this: [MATH]n(n-1)/2[/MATH], thanks
 
Hi, could someone please explain how this: [MATH]n!/2!(n-2)![/MATH] gets to this: [MATH]n(n-1)/2[/MATH], thanks
  1. Write the first four terms of n!, starting from n = ?

  2. Write the first four terms of (n-2)! starting from (n-2) = ?

What do you get when you divide (1) by (2)?
 
Hi, could someone please explain how this: thanks

Hi, could someone please explain how this: [MATH]n!/2!(n-2)![/MATH] gets to this: [MATH]n(n-1)/2[/MATH], thanks

You have to type the first denominator in grouping symbols, because as written, it does not mean as you intended:

[MATH]n!/[2!(n-2)!][/MATH] gets to this: [MATH]n(n-1)/2[/MATH]
 
Hi, could someone please explain how this: [MATH]n!/2!(n-2)![/MATH] gets to this: [MATH]n(n-1)/2[/MATH]
I think the best way to learn about these is to do some: consider 7!5!=765432154321=76\displaystyle \dfrac{7!}{5!}=\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{5\cdot4\cdot3\cdot2\cdot1}=7\cdot 6 Do you see that?

Now consider 7!2!(72)!=76543212!(54321)=762!\displaystyle \dfrac{7!}{2!(7-2)!}=\dfrac{7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1}{2!(5\cdot4\cdot3\cdot2\cdot1)}=\dfrac{7\cdot 6}{2!}

Does it now make sense that n!2!(n2)!=n(n1)2!  ?\displaystyle \dfrac{n!}{2!(n-2)!}=\dfrac{n\cdot(n-1)}{2!}~~?

 
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