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  • How many ways are possible to distribute 8 distinct books among 3 students, such that each of them gets at least one?Option: 1 4250<div

How many ways are possible to distribute 8 distinct books among 3 students, such that each of them gets at least one?

Option: 1

4250


Option: 2

 3190


Option: 3

5796


Option: 4

5440


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 books \mathrm{n=8}
number of students \mathrm{r=3}

  Using the equation, we obtain:

\mathrm{3^{8}-3 c_{1}(3-1)^{8}+3 c_{2}(3-2)^{8}=5796}

Total number of ways: 5796

 

Posted by

Divya Prakash Singh

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