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Statement-1: The number of ways distribu...

Statement-1: The number of ways distributing 10 identical balls in 4 distinct boxes such that no box is empty, is `.^(9)C_(3)`.
Statement-2: The number of ways of choosing any 3 places from 9 different places is `.^(9)C_(3)`.

A

Statement-1 is True, Statement-2 is true, Statement-2 is a correct explanation for Statement-1.

B

Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.

C

Statement-1 is True, Statement-2 is False.

D

Statement-1 is False, Statement-2 is True.

Text Solution

Verified by Experts

The number of ways of distributing n items among r persons such that each person receives at least one item is `""^(n-1)C_r-1)`.
Therefore, the number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is `""^(10-1)C_(4-1)=""^(9)C_(3)`.
So, statement-1 is true.
Clearly, statement-2 is also true but it is not a correct explanation for statement-1.
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