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Question Number 21406 by Tinkutara last updated on 23/Sep/17

Find the number of ways in which n  distinct balls can be put into three  boxes so that no two boxes remain  empty.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{in}\:\mathrm{which}\:{n} \\ $$$$\mathrm{distinct}\:\mathrm{balls}\:\mathrm{can}\:\mathrm{be}\:\mathrm{put}\:\mathrm{into}\:\mathrm{three} \\ $$$$\mathrm{boxes}\:\mathrm{so}\:\mathrm{that}\:\mathrm{no}\:\mathrm{two}\:\mathrm{boxes}\:\mathrm{remain} \\ $$$$\mathrm{empty}. \\ $$

Commented by mrW1 last updated on 06/Oct/17

are the three boxes identical?

$$\mathrm{are}\:\mathrm{the}\:\mathrm{three}\:\mathrm{boxes}\:\mathrm{identical}? \\ $$

Commented by Tinkutara last updated on 06/Oct/17

Yes.

$$\mathrm{Yes}. \\ $$

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