Answer
$252$
Work Step by Step
$C(n,r)$ denotes the number of combinations of a set of $n$ objects taken $r$ at a time, which is given by the formula:
$$C(n,r)=\dfrac{n!}{(n-r)! r !}$$
Using the formula above with $n==10$ and $r=5$ yields:
$$C(10,5)=\dfrac{10!}{(10-5)! 5 !}=\dfrac{10 \times \times 9 \times 8 \times 7 \times 6 \times 5!}{5! \cdot 5 \times 4 \times 3 \times 2 \times 1 }=252$$
