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  • How many ways are possible to distribute 5 bananas among 3 monkeys, such that each of them gets at least one?Option: 1 150<div class='q

How many ways are possible to distribute 5 bananas among 3 monkeys, such that each of them gets at least one?

Option: 1

150


Option: 2

 131


Option: 3

196


Option: 4

180


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 bananas \mathrm{n=5}
number of monkeys \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

shivangi.bhatnagar

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