factorial reductions- help!

maggiejdyer wrote:How does 12!/10! X 10!/11! x 3!/4! reduce to 12x11/1 x 1/11 x 1/4? Seeing the steps would be helpful.

12!/10! = (12)(11)(10)(9)(8)....(3)(2)(1)/(10)(9)(8)....(3)(2)(1)
= (12)(11) [the blue values cancel out]

10!/11! = (10)(9)(8)....(3)(2)(1)/(11)(10)(9)(8)....(3)(2)(1)
= 1/11 [the blue values cancel out]

3!/4! = (3)(2)(1)/(4)(3)(2)(1)
= 1/4 [the blue values cancel out]

Cheers,
Brent

Hi maggiejdyer,

This calculation actually reduces further (and the overall calculation can be reduced using a different set of steps, if you so choose). Here's how:

First, to reduce it further, we have to look at the existing result:

(12)(11)(1/11)(1/4) = (12x11)/(11x4)

Here, the 11s cancel out, leaving us with 12/4, which then reduces to 3
--------------
With the original calculation, we can reduce it in a different set of steps (but with the same math rules):

(12!/10!)((10!/11!)(3!/4!)

In the original calculation, the 10!s cancel be cancelled out first, leaving...

(12!)(1/11!)(3!/4!)

12!/11! = 12.....

(12)(3!/4!)

As noted earlier, 3!/4! = 1/4, so...

12(1/4) = 3

This goes to show that many of the calculations that you will have to do to answer GMAT Quant questions can be done in a variety of ways.

GMAT assassins aren't born, they're made,
Rich