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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 chickens are in adjacent cages? (Two animals of the same species are considered distinguishable.)

 Mar 24, 2021
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The 4 chickens can be arranged in their group together in 24 ways

  then the group of four can be placed 8 ways in the line up of 11 animals

 

24 * 11   so far

THEN the other 6 places can be arranged in 720 ways

 

720 * 24 * 11    ways total

 Mar 24, 2021

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