# Choosing K out of N Objects Formula Question

• June 8th 2013, 06:03 PM
divinelogos
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.
• June 8th 2013, 06:51 PM
Plato
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:
$\begin{array}{*{20}{c}} {{n^k}}&{n(n - 1) \cdots (n - k + 1)} \\ {\binom{n-1+k}{k}}&{\binom{n}{k}} \end{array}$
Is that correct?

If so the "upper right hand formula" is the permutation of $N$ choosing $k$.
i.e. $_N\mathcal{P}_k=\frac{N!}{(N-k)!}$.
• June 8th 2013, 07:18 PM
divinelogos
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 :)