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  • In how many ways 5 different dresses can be distributed among 3 persons so that each one gets at least one dress?Option: 1 243<br

In how many ways 5 different dresses can be distributed among 3 persons so that each one gets at least one dress?

Option: 1

243


Option: 2

260


Option: 3

150


Option: 4

180


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 dresses \mathrm{n= 5}
number of persons \mathrm{r=3}

Using the equation, we obtain:

\mathrm{3^{5}-3 c_{1}(3-1) 5+3 c_{2}(3-2) 5=243-3(25)+3(1)=150}

Total number of ways: 150

 


 

Posted by

Sumit Saini

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