Solve for: (n !)/((n-4) !)

Expression: $\frac{ n ! }{ \left( n-4 \right) ! }$

Use $n !=n \times \left( n-1 \right) !$ to expand the expression

$\frac{ n \times \left( n-1 \right) \times \left( n-2 \right) \times \left( n-3 \right) \times \left( n-4 \right) ! }{ \left( n-4 \right) ! }$

Cancel out the common factor $\left( n-4 \right) !$

$n \times \left( n-1 \right) \times \left( n-2 \right) \times \left( n-3 \right)$

Distribute $n$ through the parentheses

$\left( {n}^{2}-n \right) \times \left( n-2 \right) \times \left( n-3 \right)$

Simplify the expression

$\left( {n}^{3}-2{n}^{2}-{n}^{2}+2n \right) \times \left( n-3 \right)$

Collect like terms

$\left( {n}^{3}-3{n}^{2}+2n \right) \times \left( n-3 \right)$

Simplify the expression

${n}^{4}-3{n}^{3}-3{n}^{3}+9{n}^{2}+2{n}^{2}-6n$

Collect like terms

${n}^{4}-6{n}^{3}+9{n}^{2}+2{n}^{2}-6n$

Collect like terms

${n}^{4}-6{n}^{3}+11{n}^{2}-6n$