Question

the happy valley kennel has 4 chickens, 2 dogs, and 5 cats. (some people in happy valley like to keep chicke~ as pets!) in how many ways can the 11 animals be placed in a row of 11 cages, such that all of the arumals of each type are in adjacent cages?

Answer 1

There is only one way to place the animals in a row of 11 cages such that all of the animals of each type are in adjacent cages.

Step-by-step explanation:

To find the number of ways the animals can be placed in a row of 11 cages, we need to consider the arrangement of each type of animal separately.

Since we want all the animals of each type to be adjacent, we can consider the different arrangements of each type of animal as a single entity.

Therefore, we have three entities: chickens, dogs, and cats.

For the chickens, there is only 1 way to arrange them in a row of 4 cages since they need to be adjacent. Similarly, there is only 1 way to arrange the 2 dogs and 1 way to arrange the 5 cats.

Now, we need to consider the arrangement of these three entities.

Since there are three entities and each has only one way to be arranged, the total number of ways is 1 x 1 x 1 = 1.

Therefore, there is only one way to place the animals in a row of 11 cages such that all of the animals of each type are in adjacent cages.