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Judge revokes bail for Turtleboy blogger Aidan Kearney amid new assault ...

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Judge revokes bail for Turtleboy blogger Aidan Kearney amid new assault ...
Karen Read Reporter Aidan Kearney aka Turtle Boy ASSAULTED Amid John O ...
Aiden 'Turtleboy' Kearney Pleads The Fifth At Karen Read Hearing ...
Aiden ‘Turtleboy’ Kearney Speaks With Karen Read’s Attorney, Alan Jackson
Aiden Kearney (Turtleboy) Hearing of Nov. 28th at Stoughton District ...

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Solution: This is equivalent to partitioning 7 distinguishable widgets into 4 non-empty, unlabeled subsets. This is given by the Stirling numbers of the second kind, $S(7, 4)$, and since the zones are indistinguishable, we do not multiply by any permutation factor. From known values:
Thus, there are 350 distinct ways to distribute the widgets into the indistinct zones with no empty zone.
Question: An entomologist is studying a population of 12 bees, selecting a sample of 5 for genetic analysis. Among the bees, 4 are tagged for tracking, and we want to ensure at least one tagged bee is included in the sample. How many such samples are possible?

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