1.

10 mangoes are to be distributed among 5 persons. The probability that at least one of them will receive none, isA. `(35)/(143)`B. `(108)/(143)`C. `(18)/(143)`D. `(125)/(143)`

Answer» Correct Answer - D
10 mangoes can be distributed among 5 persons in `.^(10+5-1)C_(5-1)= .^(14)C_(4)` ways.
`therefore` Total number of elementary events `= .^(14)C_(4)`
Required probability
=1 - Probability that each person receives at least one mango
`=1- (.^(10-1)C_(5-1))/(.^(14)C_(4))=1-(.^(9)C_(4))/(.^(14)C_(4))=1-(18)/(143)=(125)/(143)`


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