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The Happy Valley Kennel has 4 chickens, 2 dogs, and 5 cats. (Some people in Happy Valley like to keep chickens as pets!) In how many ways can the 11 animals be placed in a row of 11 cages, such that all of the animals of each type are in adjacent cages? (Two animals of the same species are considered distinguishable.)

 Sep 20, 2020
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\(4!\cdot2!\cdot5!\cdot3!\implies24\cdot2\cdot120\cdot6\implies34560\)

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 Sep 21, 2020

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