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  • How many ways are possible to distribute 9 objects among 5 persons, such that each of them gets at least one?Option: 1 345630

How many ways are possible to distribute 9 objects among 5 persons, such that each of them gets at least one?

Option: 1

345630


Option: 2

131072


Option: 3

 196830


Option: 4

834120


Answers (1)

best_answer

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= 9}
number of persons \mathrm{r=5}

Using the equation, we obtain:

\mathrm{5^{9}-5 c_{1}(5-1)^{9}+5 c_{2}(5-2)^{9}-5 c_{3}(5-3)^{9}+5 c_{4}(5-4)^{9}=834,120}

Total number of ways: 834120

 

 

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Anam Khan

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