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  • No : of ways in which 6 distinct objects can be put into 2 identical boxes so that no box remains empty?Option: 1 36<div class='qna-opt

No : of ways in which 6 distinct objects can be put into 2 identical boxes so that no box remains empty?

Option: 1

36


Option: 2

26


Option: 3

55


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 objects \mathrm{n=6}
number of boxes \mathrm{r=2} 

Using the equation, we obtain:

\mathrm{2^{6}-2 c_{1}(2-1)^{6}=62}

Total number of ways: 62

Posted by

Sayak

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