Statement I: The number of ways of distributi | vedclass

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(A) Statement $I$: The number of ways of distributing $n$ identical items into $r$ distinct boxes such that no box is empty is given by the formula ${

Vedclass · Accepted Answer

Statement $I$ is true,statement $II$ is true,statement $II$ is not a correct explanation for statement $I$

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(A) Statement $I$: The number of ways of distributing $n$ identical items into $r$ distinct boxes such that no box is empty is given by the formula ${}^{n-1}C_{r-1}$.Here,$n = 10$ and $r = 4$.So,the number of ways is ${}^{10-1}C_{4-1} = {}^9C_3$.Thus,Statement $I$ is true.Statement $II$: The number of ways of choosing $r$ items from $n$ distinct items is ${}^nC_r$.For choosing $3$ places from $9$ different places,the number of ways is ${}^9C_3$.Thus,Statement $II$ is true.Since Statement $II$ is a standard combinatorial formula and not the logical derivation for the specific distribution problem in Statement $I$,Statement $II$ is not the correct explanation for Statement $I$.

Statement $I$: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is ${}^9C_3$.
Statement $II$: The number of ways of choosing $3$ places from $9$ different places is ${}^9C_3$.

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Statement $I$: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is ${}^9C_3$.Statement $II$: The number of ways of choosing $3$ places from $9$ different places is ${}^9C_3$.