What is the number of ways of distributing?
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The number of ways of distributing n identical objects among rgroups such that each group can have 0 or more (≤n) objects
I know that standard way of doing this is to solve the problem of distributing n identical objects and (r−1) partitions among themselves which can be done in C(n+r−1,r−1) ways.
But I am unable to prove to myself why it is not (r+1)n. Because each of the n objects has r+1 choices, either group1, group2,... group r or none at all.
I know that standard way of doing this is to solve the problem of distributing n identical objects and (r−1) partitions among themselves which can be done in C(n+r−1,r−1) ways.
But I am unable to prove to myself why it is not (r+1)n. Because each of the n objects has r+1 choices, either group1, group2,... group r or none at all.
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