If you remember what n! means, you can do some messy calculations quickly or compute problems that are too large for your calculator’s memory. For instance, if you wanted to calculate $\frac { 9 ! } { 6 ! }$, you could use the $n!$ button on your calculator and find that $9! = 362,880$ and $6! = 720$, so $\frac { 9 ! } { 6 ! } = \frac { 362,880 } { 720 } = 504$. You could also use a simplification technique. Since $9! = 9 ⋅ 8 ⋅ 7 ⋅ 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1$ and $6! = 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1$, you can rewrite $\frac { 9 ! } { 6 ! } = \frac { 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 } { 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1 }$ $= 9 ⋅ 8 ⋅ 7 = 504$.

Use this simplification technique to simplify each of the following problems before computing the result.