Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: unique ordering
Replies: 9   Last Post: May 10, 2014 1:16 PM

 Messages: [ Previous | Next ]
 Math Lover Posts: 66 Registered: 4/9/14
Re: unique ordering
Posted: May 10, 2014 12:17 PM

> Thought experiment:
>
> Lets say that I randomly draw N letters out of a Scrabble letter-bag. I will then
> place those letters in a horizontal line on a table. How many UNIQUE patterns of
> letters can I produce? If there were no duplicates it would be easy (N factorial)
> but when there are duplicate letters it seems more complicated.

Let's start with two letters, you have "m" of one and "n" of the
other. So the total number to place them is (m+n)!, but you
have to divide by m! to account for the fact that all different
orderings of the "m's" yield the same word, and you have to also
divide by n! for the same reason; so it's

(m+n)!
------
m!n!

You can also think about it as choosing "m" place for the first
letters and "n" for the other, so it's clearly (n+m choose n).

The general case is exactly the same.

Cheers, L.

Date Subject Author