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  • How many ways are possible to distribute 6 distinct prizes among 3 students, such that each of them gets at least one?Option: 1 250<div

How many ways are possible to distribute 6 distinct prizes among 3 students, such that each of them gets at least one?

Option: 1

250


Option: 2

190


Option: 3

396


Option: 4

540


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 prizes \mathrm{n=6}
number of students \mathrm{r=3}

Using the equation, we obtain:

\mathrm{3^{6}-3 c_{1}(3-1)^{6}+3 c_{2}(3-2)^{6}=540}

Total number of ways: 540

 

Posted by

avinash.dongre

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