P&C B&B 3: No of ways of distributing n distinct balls in r identical boxes (Sterling number method)

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Balls & Boxes-3: P&C: Number of ways of distributing 5 distinct balls in 3 identical boxes such that no box is empty.
General formula to find number of ways of distributing n distinct balls in r identical boxes such that no box is empty (Sterling number method). Support the channel:
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