Question

write the following in terms of factorilas :-
8*7*6*5

Answer 1

8*7*6*5 = $\frac{8*7*6*5*4*3*2*1}{4*3*2*1}$
           =  $\frac{8!}{4!}$

Answer 2

To write in the form of factorial of a number n, you need to multiply the numbers from 1 to n.
So to write 8*7*6*5 as factorial, we have to multiply the numbers from 1 to 4 too. And we can keep the value unaltered by dividing it with the same numbers we multiply. Thus

$8 \times 7 \times 6 \times 5\\ \\=8 \times 7 \times 6 \times 5 \times [ \frac{4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} ]\\ \\= \frac{8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{4 \times 3 \times 2 \times 1} \\ \\=\boxed{ \frac{8!}{4!} }$