[INST] 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.)/n [/INST]  ###Response: To solve this problem, we first need to consider each group of animals separately. There are three groups of animals: chickens, dogs, and cats. We can order these groups in 3! ways.

Next, we need to order the individual animals within each group. There are 4! ways to arrange the chickens, 2! ways to arrange the dogs, and 5! ways to arrange the cats.

Multiplying all these values together, we get the total number of ways to arrange the animals: 3! x 4! x 2! x 5! = 34,560.