# Number of combinations with limited repetition

by EmileMaras
Tags: combinations, combinatorics, limited, number, repetition
 P: 2 Hello I have the following combinatoric problem : I want to distribute n (equivalent) atoms among M distinct objects. Each object can contain from 0 to nlim atoms. How many combination do I have for this system? If nlim>n, this problem actually corresponds to the classical "Number of combinations with repetition". But in my case nlim
 P: 734 For the first atom,there is M choices...for the second,again M choices...for the third,again M choices...and so on! So there is always M possible choices and all that we should do is to multiply the number of choices for each of the atoms which becomes $M^n$. But because the atoms are identical,we should decrease this amount by dividing it by $n!$.
 P: 2 I guess that it is not the correct answer. Maybe I did not state my problem properly, so I will just give an exemple. Let's say I have n=3 atoms and M=3 object. An object can contain at max nmax=2 atoms. Then the possible combinations are 111, 012, 021, 102, 120, 201, 210 (where xyz gives the number of atom in each object) which corresponds to 7 combinations.
P: 734

## Number of combinations with limited repetition

 Quote by EmileMaras I guess that it is not the correct answer. Maybe I did not state my problem properly, so I will just give an exemple. Let's say I have n=3 atoms and M=3 object. An object can contain at max nmax=2 atoms. Then the possible combinations are 111, 012, 021, 102, 120, 201, 210 (where xyz gives the number of atom in each object) which corresponds to 7 combinations.
Yeah,my answer is wrong.It even gives a non-integral value!
Anyway,Check here!

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