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  • The total number of ways in which 5 frocks of different colours can be distributed among 4 baby girls so that each baby girl gets at least one frock.Option: 1</s

The total number of ways in which 5 frocks of different colours can be distributed among 4 baby girls so that each baby girl gets at least one frock.

Option: 1

239


Option: 2

240


Option: 3

241


Option: 4

341


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=5}
Number of person, \mathrm{r=4}

Therefore, total number of ways

\mathrm{=4^{5}-\left(\begin{array}{l} 4 \\ 1 \end{array}\right)(4-1)^{5}+\left(\begin{array}{l} 4 \\ 2 \end{array}\right)(4-2)^{5}-\left(\begin{array}{l} 4 \\ 3 \end{array}\right)(4-3)^{5}}

\mathrm{=1025-(4 \times 243)+(6 \times 32)-4}

\mathrm{ =1025-972+192-4 }

\mathrm{ =241}

Posted by

vishal kumar

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