Question

How many ways can you arrange 3 goats, 4 rabbits, and 5 dogs in a row?

Answer 1

@pepperkinne

Do the animals of the same type have to stay together in the row?

Answer 2

No they do not

Answer 3

Then, I would use an extended fundamental principle of counting to get the answer.

There are 12 animals total.

For the first position in the row, there are 12 choices.
After "somebody" gets into that position, then there are 11 choices for the second position.

This pattern continues to the end of the row where there will be one choice of animal for the last position.

Using the Principle,

12 * 11 * 10 * 9 * 8 *7 * 6 * 5 * 4 * 3 * 2 * 1 = ?

If you know factorial notation, then the above is an expansion of the mathematical shorthand 12! where ! means factorial.

Crank it out and post what you get. Okay? @pepperkinne