Calculate the value of \(\frac{7!}{4!}\).
There are two ways to answer this. The first is doing the factorials first, then the division:
\[\frac{7!}{4!} = \frac{5040}{24} = 210\]The other is way is valuable as well, especially as we talk about permutations and combinations in the next to pages. Here, we note that some terms will cancel out:
\[\frac{7!}{4!} = \frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{~~~~~~~~~~~4\times 3\times 2\times 1} = 7\times 6\times 5 = 210\]