The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is __________ . [2023]

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Solution

Q.
The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is __________ . [2023]

Ans.
(3483638676)

Required number of ways

$= {}^{3}{C_{0}} 3^{20} - {}^{3}{C_{1}} 2^{20} + {}^{3}{C_{2}} 1^{20}$

$= 3^{20} - 3 \times 2^{20} + 3$

$= 3 [3^{19} - 2^{20} + 1]$

$= 3483638676$

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