Question 876613
<pre>
Let's look at a different example so you'll learn how: 

C(12,5)

The 12 is the number you start the numerator with.
The 5 is the number you start the denominator with.

The 5 also tells you how many factors you need in the numerator,
as well as in the denominator. (You always have the same number
of factors in the numerator and denominator):

The numerator begins with 12 and has 5 factors, each one is
one less than the one before it, like this:

12×11×10×9×8

The denominator begins with 5 and also has 5 factors, each one is
one less than the one before it, like this:

5×4×3×2×1

So C(12,5) = {{{(12*11*10*9*8)/(5*4*3*2*1)}}}

Cancel the 12 in the top with the 4×3 in the bottom, like this:

C(12,5) = {{{(cross(12)*11*10*9*8)/(5*cross(4*3)*2*1)}}}

You can also cancel the 10 in the top with the 5×2 in the bottom

C(12,5) = {{{(cross(12)*11*cross(10)*9*8)/(cross(5)*cross(4*3)*cross(2)*1)}}} 

so the answer is

C(12,5) = 11×9×8 = 792

You can always cancel the denominator entirely into the numerator.

-----------------------------------

Edwin</pre>