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  • The total number of ways in which 6 balloons of different colours can be distributed among 3 children so that each child gets at least one balloon.Option: 1</str

The total number of ways in which 6 balloons of different colours can be distributed among 3 children so that each child gets at least one balloon.

Option: 1

520


Option: 2

 530


Option: 3

540


Option: 4

550


Answers (1)

best_answer

Given that,

The number of ways of distributing can be computed by the formula:

\mathrm{=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 frocks, \mathrm{n=6}
Number of person, \mathrm{n=3}

Therefore, total number of ways

\mathrm{=3^{6}-\left(\begin{array}{l} 3 \\ 1 \end{array}\right)(3-1)^{6}+\left(\begin{array}{l} 3 \\ 2 \end{array}\right)(3-2)^{6} }
\mathrm{=729-(3 \times 64)+3 }
\mathrm{=729-192+3 }
\mathrm{=540 }

Posted by

Ritika Harsh

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