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  • In how many ways can 5 distinct books be distributed into 2 identical shelves without leaving any of them empty?Option: 1 30<

In how many ways can 5 distinct books be distributed into 2 identical shelves without leaving any of them empty?

Option: 1

30


Option: 2

26


Option: 3

25


Option: 4

 62


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 books \mathrm{n=5}
number of shelves \mathrm{r=2}

Using the equation, we obtain:

\mathrm{2^{5}-2 c_{1}(2-1)^{5}=30}

Total number of ways: 30

 

 

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