# (10-n)!/(8-n)! ?

1. Nov 5, 2005

### Erzeon

How does ((10-n)!)/((8-n)!) = (10-n)(9-n)? I take my 2nd exam tomorrow and I came across this question

2. Nov 5, 2005

### Tom Mattson

Staff Emeritus
First state the definition of the factorial function, then apply it to (10-n)! .

3. Nov 5, 2005

### Erzeon

What do you mean by definition?

Do you mean the whole entire equation?

If so, it was ((10-n)!)/((8-n)!) >= 9

then it somehow became (10-n)(9-n) >= 9

4. Nov 5, 2005

### Erzeon

I think I found out, is it because if you expand the factorials out all the way to 0, the (8-n),(7-n),(6-n),(5-n),(4-n),(3-n),(2-n),(1-n) all cancel out in the numerator and denominator? So (10-n) and (9-n) is left?

5. Nov 5, 2005

### six789

that question is so easy!!!
you know the definition of factorial right? (n(n-1)...3*2*1)
so if you encounter that kind of problem just apply waht you learn from the factorial...
Left Side

((10-n)!)-->> you can right this as ((10-n)!)((9-n)!)((8-n)!)...((1-n)!)
and ((8-n)!)-->> you can right this as ((8-n)!)...((1-n)!)

so, if you see ((8-n)!) in the numerator and denominator, it cancels out.
therefore left side = right side...
(10-n)(9-n) = (10-n)(9-n)

6. Nov 5, 2005

### Erzeon

Thanks, I was blind to not see it.

7. Nov 5, 2005

### six789

exactly!!! see it is so easy right?

8. Nov 5, 2005

### six789

no problem... we are all here to benefit frm each others knowledge...

9. Nov 5, 2005

### Tom Mattson

Staff Emeritus
I meant just what I said: What is the definition of the factorial function function f(n)=n! .

Yes, but we do have rules here, which you all agreed to. We don't give assistance until the person asking the question shows an attempt at the problem. Guiding quesitons are OK, but complete solutions are not.

10. Nov 5, 2005

### six789

ok then mr. tom mattson...

11. Nov 5, 2005

### Erzeon

Dont worry, I had an attempt at the solution before, I asked because I got stuck and didn't think to expand it. What I really needed was a quick answer because my final high school maths exam is on tomorrow and it counts towards my score that determines what courses I can get into.

Yeh it was easy lol, I tried to think of the answer last night while going to sleep but was too tired.:D

12. Nov 5, 2005

### six789

lol... can u check my post, see if you can do it?

13. Nov 5, 2005

### Erzeon

yeh I can, thanks to both of you:D

14. Nov 5, 2005

### six789

can u check if it is correct.., reply on my post, not here...