Question

will give medal and become fan!
What is the value of the expression:
8!/6!*2!

A.1
B.28
C. 56
D. 3360

Answer 1

@Whitemonsterbunny17

Answer 2

\[\frac{8!}{6!2!}=\frac{8\times7\times6\times5\times4\times3\times2\times1}{6\times5\times4\times3\times2\times1\times2\times1}\]

\[\frac{8\times7\times\cancel{6}\times\cancel{5}\times\cancel{4}\times\cancel{3}\times\cancel{2}\times\cancel{1}}{\cancel{6}\times\cancel{5}\times\cancel{4}\times\cancel{3}\times\cancel{2}\times\cancel{1}\times2\times1}\]

\[=\frac{8\times 7}{2\times 1}=4\times7=28\]

Answer 3

Zarkon's answer was totally awesome and explains it fully, so don't think what I'm about to say takes away from it at all.

Instead, I wanted to add a little note that will help you simplify calculations with division of factorials.

See, instead of writing it all out and crossing it out, you can sort of pull the highest number out of one of the factorials if it's near another one. For example: \[\LARGE \frac{25!}{22!}\] No one would want to write that out, but if we can pull out the first 3 numbers we really see: \[\LARGE \frac{(25*24*23)*22!}{22!}=25*24*23\] A nice trick to help you from getting lost in a sea of a ton of numbers.