Question

how many different ways can you choose three vowels out of the box, if there are 5 vowels in the box and others dont matter

Answer 1

C(n,p) gives the number of ways of selcting p objects from n objects

Answer 2

so here its C(5,3) = 5*4*3/(3!) =10

Answer 3

5!/2! *3!

Answer 4

and to continue as @matricked said
c(n,p) is given by
\[c(n,p)=\left(\begin{matrix}5 \\ 3\end{matrix}\right)=\dfrac{n!}{p!(n-p)!}\]

Answer 5

such as n!=1×2×3×4....×n