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  • In how many ways 9 distinct crayons can be distributed among 3 students so that each one gets at least one?Option: 1 18150<div class='q

In how many ways 9 distinct crayons can be distributed among 3 students so that each one gets at least one?

Option: 1

18150


Option: 2

12150


Option: 3

19683


Option: 4

6561


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 crayons \mathrm{n=9}
number of students \mathrm{r=3} 

Using the equation, we obtain:

\mathrm{3^{9}-3 c_{1}(3-1)^{9}+3 c_{2}(3-2)^{9}=18150}

Total number of ways: 18150

 

 

 

Posted by

Ajit Kumar Dubey

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