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Distribution of n things among r persons...

Distribution of n things among r persons with all possible scenario

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The number of ways of distributing 50 identical things among 8 persons in such a way that three of them get 8 things each,two of them get 7 things each and remaining 3 get 4 things each,is equal to

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Statement-1: The number solutions of the equations x+y+z=15 in the set N of all natural numbers is ""^(4)C_(2) . Statement-2: The number of ways of distributing n identical items among r persons is ""^(n+r-1)C_(r-1)

The number of ways of distributing 15 things to 4 persons each receiving at least two is