Factorials !!!

The expression is $\dbinom{6}{4}$ which is essentially $\dfrac{6×5}{2} = \color{#3D99F6}{\boxed{15}}$

$?=\frac{6!}{2! \times 4!}$ $=\frac{1 \times 2 \times 3 \times 4 \times 5 \times 6}{ 1 \times 2 \times 1 \times 2\times 3 \times 4}$ $=3 \times 5$ $=15$

$x = \frac{6!}{2!\times4!}$

Expand the numerator: $x = \frac{6\times5\times4!}{2!\times4!}$

Reduce: $x = \frac{6\times5}{2!}$

Since $2! = 2\times1$ , then we have $x = \frac{30}{2}$

Therefore $x = 15$ , our solution.

6!= 4! x 30

6!/ 2! x 4! = 4! X 30 / 2! x 4! = 30 / 2! = 30 / 2 = 15