# How do you calculate combinations of 10 numbers?

Nov 27, 2014

If $r$ numbers are chosen, then the number of all combinations can be found by

C(10,r)={P(10,r)}/{r!}={10 cdot 9 cdot cdots cdot (10-r+1)}/{r!}

Example

If $r = 3$, then

$C \left(10 , 3\right) = \frac{10 \cdot 9 \cdot 8}{3 \cdot 2 \cdot 1} = 120$ combinations

I hope that this was helpful.