Number of ways in which five identical balls can be distributed among ten identical boxes such that

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6.Permutation and Combination

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The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

$10 !$

$\frac{{10\,!}}{{5\,!}}$

$\frac{{10\,!}}{{{{(5\,!)}^2}}}$

None of these

(IIT-1973)

Solution

(c) Out of $10$ boxes we have to choose only $5$ boxes because the balls are identical and the boxes are also identical (but they can occupy different places), the required number of ways ${ = ^{10}}{C_5} = \frac{{10\;!}}{{{{(5\;!)}^2}}}$.

Standard 11

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(JEE MAIN-2021)

The number of ways in which five identical balls can be distributed among ten identical boxes such that no box contains more than one ball, is

Solution

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A committee of $7$ has to be formed from $9$ boys and $4$ girls. In how many ways can this be done when the committee consists of:

at most $3$ girls?