Find $$$C{\left(10,3 \right)}$$$

Find the number of combinations without repetitions $$$C{\left(10,3 \right)}$$$.

The formula is $$$C{\left(n,r \right)} = \frac{n!}{r! \left(n - r\right)!}$$$.

We have that $$$n = 10$$$ and $$$r = 3$$$.

Thus, $$$C{\left(10,3 \right)} = \frac{10!}{3! \left(10 - 3\right)!} = 120$$$ (for calculating the factorial, see factorial calculator).

$$$C{\left(10,3 \right)} = 120$$$