Solution to dividing apples

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1 total messages Started by padmanab Wed, 27 Jan 1993 18:21

#2691

Author: padmanab
Date: Wed, 27 Jan 1993 18:21

24 lines
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>I had posted the following problem last week: 

>Suppose there are 25 identical apples. How many 
>ways can you divide them among three people? 

The reason I posted it was because I saw a vey 
interesting solution to this problem.  

Add two identical `oranges' to this collection 
of apples. The total number of ways of arranging 
this new collection (i.e., permutations) is 

FACTORIAL(25+2) / ( FACTORAL(25)*FACTORIAL(2) )

Now observe that each of the permutation is a way of 
dividing the apples among three people!! 

Of course this can be generalized into the problem of 
dividing `n' similar objects among `m' people. 

-Prasad Padmanabhan
Dept. of ECE
University of Massachusetts
Amherst MA 01003

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