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  • In how many ways can seven bangles, each of a different colour, be distributed among five distinct boxes such that no box remains empty?Option: 1</stro

In how many ways can seven bangles, each of a different colour, be distributed among five distinct boxes such that no box remains empty?

Option: 1

17900


Option: 2

17800


Option: 3

16900


Option: 4

 16800


Answers (1)

best_answer

Given that,

Number of bangles, \mathrm{n=7}
Number of boxes, \mathrm{r=5}

Therefore, the total number of ways

\mathrm{=5^{7}-\left(\begin{array}{l} 5 \\ 1 \end{array}\right)(5-1)^{7}+\left(\begin{array}{l} 5 \\ 2 \end{array}\right)(5-2)^{7}-\left(\begin{array}{l} 5 \\ 3 \end{array}\right)(5-3)^{7}+\left(\begin{array}{l} 5 \\ 4 \end{array}\right)(5-4)^{7}}

\mathrm{=78125-(5 \times 16384)+(10 \times 2187)-(10 \times 128)+5}

\mathrm{ =78125-81920+21870-1280+5}

\mathrm{ =16800}

 

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Gunjita

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