5Question: An entomologist studies 6 species of bees and 4 species of butterflies. If she wants to select 3 species for a pollination experiment, with at least 1 bee and 1 butterfly, how many distinct groups can she form?

March 11, 2026

5Question: An entomologist studies 6 species of bees and 4 species of butterflies. If she wants to select 3 species for a pollination experiment, with at least 1 bee and 1 butterfly—how many distinct groups can she form?

As pollination science takes center stage in discussions about ecosystem health and food security, questions about how researchers strategically choose species for study are gaining traction. This particular puzzle—identifying combinations of insect species for pollination experiments

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Question: An archaeologist discovers 7 distinct pottery shards from a Peruvian site and 5 from a Mesoamerican site. If she arranges them in a row on a shelf with all Peruvian shards indistinct and all Mesoamerican shards indistinct, how many distinct arrangements are possible?
Solution: The problem reduces to permutations of a multiset. There are $ 7 + 5 = 12 $ total shards, with 7 identical Peruvian and 5 identical Mesoamerican. The number of distinct arrangements is $
Question: A hydrologist models groundwater flow through 3 layers of soil, each with 2 possible flow channels (A or B). If the system must have exactly 2 channels flowing vertically and 1 horizontally, how many distinct flow configurations are possible?

5Question: An entomologist studies 6 species of bees and 4 species of butterflies. If she wants to select 3 species for a pollination experiment, with at least 1 bee and 1 butterfly, how many distinct groups can she form?

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