What is #(5!3!)/(6!)#?

2 Answers
Apr 30, 2018

#1#

Explanation:

This problem can be made easier by rewriting the equation:

#(5 * 4 * 3 * 2 * 1 * 3 * 2 * 1)/( 6 * 5 * 4 * 3 * 2 * 1)#

We can cancel quite a few numbers:

#(cancel(5 * 4 * 3 * 2 * 1) * 3 * 2 * 1)/( 6 * cancel(5 * 4 * 3 * 2 * 1)#

#(3 * 2 * 1)/6#

#6/6 = 1#

Apr 30, 2018

The answer is #1#.

Explanation:

The ! is a factorial, which means if you have, for example, #4!#, you just do #4*3*2*1=24#.

Method 1:

Multiply the #6!# out to be #6*5!# and get #(5!3!)/(6*5!)#.
(We do this so we can cancel out the #5!#s in the next step.)
Cancel out the #5!#s and get: #(3!)/6#
Now just multiply out the #3!# to be #3*2*1=6#.
You end up with #6/6#, which equals #1#.

This looks like a lot, but it's actually quite nice because you don't have to multiply out the #5!# or #6!# completely.

Method 2:

Another way to do this is just completely multiply everything out like this:
#(5*4*3*2*1*3*2*1)/(6*5*4*3*2*1)#
Cancel everything out that you can, and you should end up with the same answer, #1#.