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  • How many ways are possible to distribute 4 distinct coloured pencils to 2 students, such that each of them gets at least one?Option: 1 25<b

How many ways are possible to distribute 4 distinct coloured pencils to 2 students, such that each of them gets at least one?

Option: 1

25


Option: 2

16


Option: 3

 14


Option: 4

18


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 pencils \mathrm{n=4}
number of students \mathrm{r=2}

Using the equation, we obtain:

\mathrm{2^{4}-2 c_{1}(2-1)^{4}=2^{4}-2=14}

Total number of ways: 14

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chirag

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