Mrs. Olson has 8 brands of cat food and 3 cats, each of which receives 1 can per day. In how many different ways can she serve the cats on any day, assuming that no 2 cats get the same brand?

Question

Mrs. Olson has 8 brands of cat food and 3 cats, each of which receives 1 can per day. In how many different ways can she serve the cats on any day, assuming that no 2 cats get the same brand?

Answer 1

This is a bit difficult to see, but the answer actually comes out to be 8P3. Make 8 slots representing the cat food. And assign the three cats to the 8 slots.

We'll assume that A, B, and C are the cats, so a possible arrangement is:

A _ _ B _ C _ _

This is different then:

B _ _ A _ C _ _

because here A and B are getting different cat food, so it's a permutation