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sholman · Apr 19, 2007, 11:05 PM

I need to know how to solve this problem, I've been stuck for an hour, please help
Question: find the indicated value of xCx-1 (it's a permutation)

asterisk_man · Apr 20, 2007, 11:37 AM

xCy would mean x Choose y and you're asking for xCx or x Choose x.

$nCk = C_k^n = {n \choose k} = \frac{n!}{k!(n-k)!}.$

so if we do xCx-1 we get:
$\frac{x!}{x!(x-x)!} -1 = \frac{x!}{x!0!} -1 = 1-1=0$

note: 0!=1 Math Forum - Ask Dr. Math

If you think about it, this makes sense because it's like saying, how many ways are there to choose x items from a group of x items. The answer is 1, choose them all.

I hope this helps and is what you were asking about.