Math CentralQuandaries & Queries


Question from Irfan, a student:

John wants to paint 4 rooms in his house, each a different color and he may choose from 7 different colors of paint.
How many color combinations are possible for the four rooms.


Note that rooms are distinguishable: painting the kitchen red and the bathroom blue is not the same as painting the kitchen blue and the bathroom red.

How many choices has he for the first room?
How many for the second? Obviously these choices depend on his choice for the first room, but does the number of choices vary?
How many ways, then , are there to do the first two rooms? If you're unsure try making a list. What operation did you use to get this number?
Now how many ways can he do the third room? (And so on)

Good Hunting!


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