Question

Evaluate each expression.
6! =
3! • 2! =
.
6!
3!
11

Answer 1

`6! = 1 * 2 * 3 * 4 * 5 * 6 =720\\\\3! \cdot 2! = (1 * 2 * 3) * (1 * 2) = 6 * 2 = 12\\\\\\(6!)/(3!) =(1 * 2 * 3 * 4 * 5 * 6)/(1 * 2 * 3) = 4 * 5 * 6=120`

Answer 2

`\begin{array}{l}6!=1 * 2 * 3 * 4 * 5 * 6 =720\\\\\\3! \cdot 2! = (1 * 2 * 3) * (1 * 2) = 6 * 2 = 12\\\\\\(6!)/(3!) =(1 * 2 * 3 * 4 * 5 * 6)/(1 * 2 * 3) = 4 * 5 * 6=120\end{array}`

Permutations Summary:

`\begin{array}{l}\rm{(i)\:n!=n(n-1)(n-2)\:...\:3*2*1}\\\\\\\rm{(ii)\:n!=n*(n-1)!}\\\\\\ \rm{(iii)\:0!=1}\end{array}`