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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Solution

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

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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