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Silly question on factorials

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
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Silly question on factorials

by tzink » Mon Jul 28, 2008 3:43 pm
I notice a lot of answer explanations on this forum involve factorials--especially on questions involving combinations or permutations.

I understand the concept of the factorial (product of 1 to n inclusive), but back in school when i used to have to use them, there was a handy little button on the calculator to calculate them.

How is it possible to know high factorials by hand in under two minutes?

Are there tricks to these problems?

Cheers
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by parallel_chase » Tue Jul 29, 2008 3:08 am
There is no short cut for this.

In GMAT particularly you dont need to concentrate on calculations.

Just remember calculations till 6! which is easy enough with practice.
2!=2
3!=6
4!=24
5!=120
6!=720
7!=5040
8!=40320
9!=362880
10!=3628800

I could do all this in less than 10 secs because i knew all the calculations till 6!.

Hope this helps
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Re: Silly question on factorials

by Ian Stewart » Tue Jul 29, 2008 7:09 am
tzink wrote:How is it possible to know high factorials by hand in under two minutes?

Are there tricks to these problems?

Cheers
The trick is, you will never, ever need to calculate a factorial higher than perhaps 7! on the GMAT. It certainly can't hurt to know factorials up to 6!, but it probably won't help much, and it doesn't take long to work out if needed. Whenever you see a large factorial, it will either be unnecessary to calculate its value, or it will be in a fraction, and there will be a lot of cancellation. For example, you might see something like:

12!/10!

Here, of course, you would not want to multiply out 12!, multiply out 10!, then finally divide- that would take all day. But if you see that 12! = 12*11*10!, you can see that we can cancel:

12!/10! = (12*11*10!)/10! = 12*11= 132

That's the way most questions with factorials work- lots of cancellation.
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by VP_RedSoxFan » Thu Jul 31, 2008 8:17 am
Ian hit it on the head. (I really like coming after this guy because he's spot on.)

The GMAT will require factorials in the context of Combination and Permutation problems. The way those formulas are set up to divide factorials before you actually calculate them.

For example:

8_C_3 = 8!/ [3!(8-3)!] = 8*7*6*5*4*3*2*1 / 3*2*1 * 5*4*3*2*1

Here the 5 through 1 factors in the numerator and denominator cancel to 1 leaving:

8*7*6 / 3*2*1

and the 3*2 in the denominator cancel the 6 factor in the numerator. That leaves simply 8*7, or 56.

I have lots of students who want to calculate 8! then divide it by 5! and 3! but canceling common factors in the numerator and denominator is WAY faster and less prone to error.

This is the manner in which factorials are tested on the GMAT.
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