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The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is

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The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is

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2 Answers

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20C3 x 3! = 20P3

Total no. of ways = 20P3 x 317

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Total - (one child receive no orange + two child receive no orange)

\(= 3^{20} - ({^3C_1} (2^{20} -2) + {^3C_21^{20}})\)

\(= 3483638676\)

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