factorial division when the bottom number is larger than the top number I have a factorials problem to solve, and I do not know the method of solving it.
I know how to do one number factorials (e.g. 5!, 15! etc...) and factorial division where the top number is larger than the bottom number.
Could someone please make a simple guide (with an example question/answer please) on how to solve a factorial divison such as:
100!/102!
I've tried so many searches on google no one has expained this type of question 
Thank you very much.
 A: Hint:
$$\dfrac{100!}{(102)!} = \dfrac{100!}{102\cdot 101\cdot 100!}$$
Cancel.
A: Let's make the numbers a little smaller and write it out:
$$\frac{10!}{12!} = \frac{10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}{12 \cdot 11 \cdot 10 \cdot 9 \cdot 8 \cdot 7 \cdot 6 \cdot 5 \cdot 4 \cdot 3 \cdot 2 \cdot 1}.$$
All but the $12$ and $11$ in the denominator cancel.  But this can be written to make this evident:
$$\frac{10!}{12!} = \frac{10!}{12 \cdot 11 \cdot 10!} = \frac{1}{132}.$$
You're still canceling all of the numbers you did in the first expression, but the notation is much more compact.
Now apply this to your problem:
$$\frac{100!}{102!} = \frac{100!}{102 \cdot 101 \cdot 100!} = \frac{1}{10302}.$$
A: If you know how to handle things when the big guy is on top, start from
$\frac{100!}{102!}$;
Flip it over: We get
$\frac{102!}{100!}$;
Simplify, which you know how to do. We get
$(101)(102)$;
Flip it over again: We get
$\frac{1}{(101)(102)}$, and now we are finished.
After a couple of times, you will be able to skip the middle steps and go immediately to the answer.
