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^ Combinations formula. Seems legit.

I do understand that, but I want to know how this can be solve with out the use of a calculator.

Factorials?

choosing 'r' out of 'n' can be written as
\[ \binom{n}{r} = {n! \over r! (n-r)!} \]

Give me another example of what we are talking about that does not involve polygons.

Very good example:
\[\left(\begin{matrix}7 \\5\end{matrix}\right)=\frac{ 7! }{ 5!(7-5)!}\]

yep!!

84

THANK YOU! That is exactly what I was looking for in the original question. Sorry if I wasn't clear.

http://www.wolframalpha.com/input/?i=7+choose+5

lol .. .no without calculator this is horrible.

What do you mean the top and bottom cancel out?

|dw:1353182495182:dw|

also when 'r' is pretty close to 'n', you can do the same.