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.