Question

how many different combinations of six people can sit in four chairs? assume one person sits in each chair

Answer 1

We want to choose 4 people and we have 6 people to choose from. This is a combination of 6, 4 by 4. Also called six choose four.

The following formula:

$_rC_n=\frac{n!}{r!(n-r)!}$

Is the combination of $r$ objects choosen from a total of $n$. It's $n$ choose $r$.

For our problem, we just need to compute the following:

$_4C_6=\frac{6!}{4!(6-4)!}=\frac{6\times5\times4!}{4!2!} =\frac{6\times5}{2\times1} =15$

Thus

$\boxed{_4C_6=15}$

Therefore the answer is 15 different combinations