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  • Find the number of ways to put 6 distinct products into 5 shelves so that no shelf should remain empty?  Option: 1 8100<

Find the number of ways to put 6 distinct products into 5 shelves so that no shelf should remain empty?

 

Option: 1

8100


Option: 2

2160


Option: 3

7290


Option: 4

1800


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 products \mathrm{n=6}
number of shelves \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

SANGALDEEP SINGH

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