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  • The total number of ways in which 5 sweets of different colours can be distributed among 3 kids so that each kid gets at least one sweet.Option: 1 12

The total number of ways in which 5 sweets of different colours can be distributed among 3 kids so that each kid gets at least one sweet.

Option: 1

120


Option: 2

150


Option: 3

130


Option: 4

160


Answers (1)

best_answer

Given that,

The number of ways of distributing can be computed by the formula:
=r^{n}-\left(\begin{array}{l} r \\ 1 \end{array}\right)(r-1)^{n}+\left(\begin{array}{l} r \\ 2 \end{array}\right)(r-2)^{n}-\ldots+(-1)^{r-1}\left(\begin{array}{c} r \\ r-1 \end{array}\right)(1)^{n}

Number of sweets, \mathrm{n=5}
Number of kids, \mathrm{r= 3}

Therefore, total number of ways
=3^{5}-\left(\begin{array}{l} 3 \\ 1 \end{array}\right)(3-1)^{5}+\left(\begin{array}{l} 3 \\ 2 \end{array}\right)(3-2)^{5}
=243-3(2)^{5}+3
=243-96+3
=150



 

Posted by

Sanket Gandhi

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