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Choosing K out of N Objects Formula Question

I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?

Attachment 28552

Sorry for the elementary question and thanks for your time.

Re: Choosing K out of N Objects Formula Question

Quote:

Originally Posted by

**divinelogos** I'm having trouble interpreting the formula that is "with regard to order" and "without replacement". How exactly would I compute the upper right hand formula with, for example, k=5 and n=10?

You really should learn to post in LaTeX. It hard to know exactly what you are asking.

Your table seems to be:

$\displaystyle \begin{array}{*{20}{c}} {{n^k}}&{n(n - 1) \cdots (n - k + 1)} \\ {\binom{n-1+k}{k}}&{\binom{n}{k}} \end{array}$

Is that correct?

If so the "*upper right hand formula*" is the permutation of $\displaystyle N$ choosing $\displaystyle k$.

i.e. $\displaystyle _N\mathcal{P}_k=\frac{N!}{(N-k)!}$.

Re: Choosing K out of N Objects Formula Question

I thought the picture would be clearer than Latex. But that seems to be correct! Thanks for the help :)