Interpretation of Multiplicity Function

[leeone]

Hi. I am trying to understand the multiplicity function Ω!/L!(Ω-L)! where Ω= number of boxes and L= number of distinguishable boxes. I just want a simple intuitive explanation. I have seen a couple of these but none of them ever stick. The term that confuses me the most is the (Ω-L)!

Any help would be greatly appreciated.

Thanks

 

[mathman]

The expression is the standard combinatorial symbol.
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
Above is a thorough easy to understand description of the subject. The last part describes exactly what you are looking for.

 

[leeone]

Awesome. I had discovered that the trick is to divide by (n-r)! in order to divide out the rest of the n!, but I guess I had forgotten. Thank you that was a great explanation. It makes complete sense now.