- #1

mindauggas

- 127

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Hello everyone

i don't see a connection why C

Is there a way to simplify them in order to see why the equality holds?

the definition of factorial being n!=1*2*...*n I expressed it as

n! = (n-(n-1))(n-(n-2))...(n-(n-n)).

Is this wrong? the idea was that (n-(n-1)) = 1 (I expressed all the factorials in the same way; tried to simplify something).

I also tried to express n!/i!(n-i)! as such: 1*2*...*n/1*2*...i*(n-i)!

This is a problem form Courant/Robbin/Stewart - "What is Mathematics" pp 17.

Thank you very much for your time and help.

## Homework Statement

i don't see a connection why C

_{i}^{n}= [itex]\frac{(n*(n-1)*(n-2)*...*(n-i+1))}{1*2*...*i }[/itex] = [itex]\frac{n!}{i!(n-i)!}[/itex]Is there a way to simplify them in order to see why the equality holds?

## The Attempt at a Solution

the definition of factorial being n!=1*2*...*n I expressed it as

n! = (n-(n-1))(n-(n-2))...(n-(n-n)).

Is this wrong? the idea was that (n-(n-1)) = 1 (I expressed all the factorials in the same way; tried to simplify something).

I also tried to express n!/i!(n-i)! as such: 1*2*...*n/1*2*...i*(n-i)!

This is a problem form Courant/Robbin/Stewart - "What is Mathematics" pp 17.

Thank you very much for your time and help.

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