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# What does the r variable represent and what does the n variable represent in math?

Updated: 9/26/2023

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Q: What does the r variable represent and what does the n variable represent in math?
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It can represent anything you want it to. The conventional use is that it represents the number of successes.

nCr=n!/r!/(n-r)!

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If an amount C is invested for n years with an interest rate of r%, then the amount of interest earned is C*n*r/100

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Assuming that x represents multiplication, it is p times r times n or prn.

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### Prove that nCr plus nCr minus 1 equals n plus 1Cr?

nCr + nCr-1 = n!/[r!(n-r)!] + n!/[(r-1)!(n-r+1)!] = n!/[(r-1)!(n-r)!]*{1/r + 1/n-r+1} = n!/[(r-1)!(n-r)!]*{[(n-r+1) + r]/[r*(n-r+1)]} = n!/[(r-1)!(n-r)!]*{(n+1)/r*(n-r+1)]} = (n+1)!/[r!(n+1-r)!] = n+1Cr