Do you know what nC5 and nC4 represent?

[dancing_math]

Homework Statement

The expression nC5/nC4 can be simplified to:

Homework Equations

I'm assuming that I'm to use n!/(n-r)!r!

The Attempt at a Solution

I attempted to do this:
n!/(n-5)!5! / n!/(n-4)!4!
n!/(n-5)!5! x (n-4)!4!/n!
1/(n-5)!5! x (n-4)!4!
And I'm stuck after this point. The possible answers are:
A. 1/5(n-5)
B. (n-4)/5
C. 5(n-5)
D. none of the above.

 

[SammyS]

Homework Statement

The expression nC5/nC4 can be simplified to:

Homework Equations

I'm assuming that I'm to use n!/(n-r)!r!

The Attempt at a Solution

I attempted to do this:
n!/(n-5)!5! / n!/(n-4)!4!
n!/(n-5)!5! x (n-4)!4!/n!
1/(n-5)!5! x (n-4)!4!
And I'm stuck after this point. The possible answers are:
A. 1/5(n-5)
B. (n-4)/5
C. 5(n-5)
D. none of the above.

Hello dancing_math. Welcome to PF !


1/(n-5)!5! x (n-4)!4! is equivalent to \displaystyle \frac{(n-4)!\,4!}{(n-5)!\,5!}\ .

You should be able to further simplify \displaystyle \frac{4!}{5!} and \displaystyle \frac{(n-4)!}{(n-5)!}\ .