Well then find the error in the book's solution.Here it is-

"No. of distributions possible(without any restrictions) is

3^12.----------(1)

No. of cases where a boy can get all the 12 fruits=3C1(any of the 3 boys can get them).Alternately,we can say that in 3 cases 2 boys won't get any fruit.-------(2)

now,if a boy gets no fruit then the other two will get them.No. of distributions possible for 2 boys=2^12.Here also a boy (of the 2) can get no fruit in 2 ways.So, no. of distributions where the 2 boys would get 12 fruits with each having at least one fruit = 2^12-2.

so,1 out of the 3 boys would get no fruit in 3C1(2^12 -2) ways--------------------(3)

From (1),(2) & (3) we get,Required no. of distributions

=Total distrbutions-(2 boys get no fruit + 1 boy gets

no fruit)

=3^12-{3+3C1(2^12-2)}

=519156.

Ans.

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I am starting to think there may be 2 correct answers.