8 rooms are to be painted with 3 blue, 3 red, and 2 yellow paint tins.(each tin of paint can paint exactly one room and all rooms are identical in shape and size). In how many ways it can be done?

1 Answer



If all the rooms were to be painted in unique colours (and so 8 in all), we'd have #8! = "40,320"# ways to paint the rooms.

But we have duplicates of the colours. To get rid of the duplicate solutions, we divide by the number of ways each colour can be internally ordered (which is the number of a coloured paint tin, factorial).

This gives:

#(8!)/(3!3!2!)="40,320"/(6xx6xx2)=560# ways