Question

In how many ways may 3 red cars, 4 blue cars, 4 yellow cars, and 2 green cars be parked so that those of the same color are parked together?

Answer 1

Hi rigo :)

Do you have some idea on how to solve this?

In how many ways can you arrange just 3 red cars??

Answer 2

I was thinking (13!/3!4!4!2!)

Answer 3

so you do have some idea, cool!

3!4!4!2! are the total ways to park those colored cars,
but now you have one bunch of red cars, one bunch of blue cars, and so on.. that you can arrange among themselves.

how many bunches of cars are there?

Answer 4

thats because
3 red cars parked first is a different way than 3 rd cars parked last!

Answer 5

now see if you get the total ways as
\(4! \times (3!4!4!2!)\)