Question

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

Answer 1

$6! = 1 \times 2 \times 3 \times 4 \times 5 \times 6 =720\\\\3! \cdot 2! = (1 \times 2 \times 3) \times (1 \times 2) = 6 \times 2 = 12\\\\\\\dfrac{6!}{3!} =\dfrac{1 \times 2 \times 3 \times 4 \times 5 \times 6}{1 \times 2 \times 3} = 4 \times 5 \times 6=120$

Answer 2

Answer:

$\begin{array}{l}6!=1 \times 2 \times 3 \times 4 \times 5 \times 6 =720\\\\\\3! \cdot 2! = (1 \times 2 \times 3) \times (1 \times 2) = 6 \times 2 = 12\\\\\\\dfrac{6!}{3!} =\dfrac{1 \times 2 \times 3 \times 4 \times 5 \times 6}{1 \times 2 \times 3} = 4 \times 5 \times 6=120\end{array}$

Permutations Summary:

$\begin{array}{l}\rm{(i)\:n!=n(n-1)(n-2)\:...\:3\times2\times1}\\\\\\\rm{(ii)\:n!=n\times(n-1)!}\\\\\\ \rm{(iii)\:0!=1}\end{array}$