The Happy Valley Kennel has 4 chickens, 1 dog, and 6 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.)

 Jul 14, 2022

There are \(4!\) ways to order the chickens 


There are \(6!\) ways to order the cats. 


There is only 1 way to order the dog. 


There are \(3!\) ways to order the chickens, cats, and dogs. 


So, there are \(4! \times 6! \times 3 = \color{brown}\boxed{51840}\) ways. 

 Jul 14, 2022

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