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  • Find the number of ways to put 6 rings in 5 boxes so that no box should remain empty?Option: 1  1800<stron

Find the number of ways to put 6 rings in 5 boxes so that no box should remain empty?

Option: 1

 1800


Option: 2

2160


Option: 3

 7290


Option: 4

8100


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 rings \mathrm{n=6}
number of boxes \mathrm{r=5}

Using the equation, we obtain:

\mathrm{5^{6}-5 c_{1} 4^{6}+5 c_{2} 3^{6}-5 c_{3} 2^{6}+5 c_{4} 1^{6}}
\mathrm{15265-(5 \times 4096)+7290-640+5=1800}

Total number of ways: 1800

Posted by

manish painkra

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