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  • How many ways are possible to distribute 8 distinct objects into 5 identical bins, so that no bin should be empty?Option: 1 368765</div

How many ways are possible to distribute 8 distinct objects into 5 identical bins, so that no bin should be empty?

Option: 1

368765


Option: 2

125640


Option: 3

555000


Option: 4

625640


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 objects \mathrm{n=8}
number of bins \mathrm{r=5}

Using the equation, we obtain:

\mathrm{5^{8}-5 c_{1}(5-1)^{8}+5 c_{2}(5-2)^{8}-5 c_{3}(5-3)^{8}+5 c_{4}(5-4)^{8}}
\mathrm{ =125640}

Total number of ways: 125640

 

 

Posted by

Kuldeep Maurya

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