How many ways can a committee of three be chosen from a group of ten people? How many ways are there to choose a president, secretary, and treasurer.
I know that on the first part I have to use the combination formula since order doesn't matter. Then
$\frac{n!}{r!(n-r)!} \rightarrow \frac{10!}{3!(10-3)!}$= 120.
The second part requires order meaning that I need to use the permutation formula
$\frac{n!}{(n-r)!}$ $\rightarrow$ $\frac{10!}{(10-3)!}$ = 720.
Is my process correct?
Best Answer
Yes, your process is correct. However, normally we to write the question as $\binom{10}{3}$ or ${^{10}\mathrm C_3}$ and the second question as ${^{10}\mathrm{P}_3}$ or $10^{\,\underline 3}$ .