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  • In how many ways can eight ice-creams, each of a different colour, be kept among five distinct cups such that no cups remain empty?Option: 1 <

In how many ways can eight ice-creams, each of a different colour, be kept among five distinct cups such that no cups remain empty?

Option: 1

135999


Option: 2

 125999


Option: 3

115999


Option: 4

105999


Answers (1)

best_answer

Given that,

Number of ice-creams,\mathrm{n=8}
Number of cups,\mathrm{r=5}

Therefore, total number of ways

\mathrm{=5^{8}-\left(\begin{array}{l} 5 \\ 1 \end{array}\right)(5-1)^{8}+\left(\begin{array}{l} 5 \\ 2 \end{array}\right)(5-2)^{8}-\left(\begin{array}{l} 5 \\ 3 \end{array}\right)(5-3)^{8}+\left(\begin{array}{l} 5 \\ 4 \end{array}\right)(5-4)^{8} }

\mathrm{=390625-(5 \times 65536)+(10 \times 6561)-(10 \times 256)+5 }

\mathrm{ =390625-327680+65610-2560+5 }

\mathrm{ =125999 }

Posted by

Irshad Anwar

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