- #1
mindauggas
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Hello everyone
i don't see a connection why Cin = [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 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 Cin = [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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