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Find the number of ways in which 13 iden...

Find the number of ways in which 13 identical apples can be distributed among 3 persons so that no two persons receive equal number of apples and each can receive any number of apples.

Text Solution

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Total number of ways of distributing apples without any restrictions
`=(13+3-1)C_(3-1)= .^(15)C_(2)=105`
But it will also contain the cases when exactly two persons receive equal number of apples.
0 0 13
1 1 11
6 6 1
Number of such ways `=7xx3=21`
Therefore, required number of ways =105-21=84
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