SOLUTION: I am really lost with this concept: Factorial expressions Find the value of the following: {{{(11! 12!)/(8!10!)}}} If your answer is not an integer, write it as an exact

Algebra ->  Probability-and-statistics -> SOLUTION: I am really lost with this concept: Factorial expressions Find the value of the following: {{{(11! 12!)/(8!10!)}}} If your answer is not an integer, write it as an exact       Log On


   

Question 548996: I am really lost with this concept:
Factorial expressions
Find the value of the following:
%2811%21+12%21%29%2F%288%2110%21%29
If your answer is not an integer, write it as an exact fraction.
Found 2 solutions by Alan3354, mathie123:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Factorial expressions
Find the value of the following:
11! 12!
-------
8! 10!
-------------
11!/10! = 11, so cancel those
= 11*12!/8!
-----------
12!/8! = 12*11*10*9
---
= 11*12*11*10*9
= 130680

Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
We know that n!=n*(n-1)*(n-2)*...*2*1
So we can expand
%2811%21+12%21%29%2F%288%2110%21%29
to get:

Now... looking at the expression above... can anything divide out (i.e. get rid of any number that appears in the numerator and denominator). This leaves:
%2811%2A12%2A11%2A10%2A9%29
Now this expression can be calculated as an integer on your calculator... I will leave that for you to do .
Obviously if we had large numbers... it wouldn't be a good idea to write out the whole factorial, but you may be able to see some patterns once you do some examples... (try to find them)
Hopefully this helps a bit... let me know if you are still unsure