Answer
a) $120$
b) $10$
Work Step by Step
a) The symbol $n!$ means the product of all the whole numbers from $1$ to $n$:
$$n!=1\cdot 2\cdot 3\cdot\dots\ \cdot n.$$
Calculate $5!$:
$$5!=1\cdot 2\cdot 3\cdot 4\cdot 5=120.$$
b) The combinations of $n$ objects taken $r$ can be written:
$$\binom{n}{r}=\dfrac{n!}{(n-r)!r!}.$$
Calculate $\binom{5}{2}$:
$$\binom{5}{2}=\dfrac{5!}{(5-2)!2!}=\dfrac{1\cdot 2\cdot 3\cdot 4\cdot 5}{1\cdot 2\cdot 3\cdot 1\cdot 2}=10.$$
