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  • In how many ways 7 distinct objects can be distributed among 4 boxes so that each one gets at least one?Option: 1  1024<

In how many ways 7 distinct objects can be distributed among 4 boxes so that each one gets at least one?

Option: 1

 1024


Option: 2

1260


Option: 3

6250


Option: 4

8400


Answers (1)

Empty box is not allowed

So, number of ways of distributing \mathrm{'n'} distinct things in \mathrm{'r'} identical places can be computed by the formula,

\mathrm{r^{n}-r c_{1}(r-1)^{n}+r c_{2}(r-2)^{n}---+(-1)^{r-1} r c_{r-1}(1)^{n}}

Here, number of objects \mathrm{n=7}
number of boxes \mathrm{r=4}

Using the equation, we obtain:

\mathrm{4^{7}-4 c_{1}(4-1)^{7}+4 c_{2}(4-2)^{7}-4 c_{3}(4-3)^{7}=8400}

Total number of ways: 8400

Posted by

Ramraj Saini

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