A father has five distinct antiques and he is thinking of giving them to his two sons. In how many ways can he do so if it is possible that he may not necessarily give away all the five antiques. Also a son may or may not receive an antique.
2026-04-28 11:14:42.1777374882
Question using Stirling numbers of second kind
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I don't see a connection to Stirling numbers of the second kind. The parent has $3$ options for each antique: Giving it to one child, to the other, or not giving it away at all. These choices are independent, so there's a total of $3^5=243$ different possibilities.