Mathematics DESTRIBUTION OF ALIKE OBJECTS

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DESTRIBUTION OF ALIKE OBJECTS

Type-1 :

Total number of ways in which `n` identical coins can be distributed among `p` persons so that each person may get any number of coin is

`text()^(n+p-1)C_(p-1)=((n+p-1)!)/((p-1)!(n)!)`

Proof:-

Let `6` identical coins can be distributed among `3` persons `R|S|G`

Type-2 :

Total number of ways in which `n` identical items can be distributed among `p` persons such that each of them receive at least one item `text()^(n-1)C_(p-1)`.