A painter is given the job of painting the doors of 5 adjacent bedrooms using 5 colours: red, blue, yellow, green and orange.
If the owner of the house insists that the doors should be painted with at most two colours, find the number of ways which the painter could have the job done.
As many regular readers here may know, I in former life I was an editor for published test questions. As such, when I read a question here I naturally assume it has been fully vetted. However, in this case I think awkward has found what the true meaning of this question: doors have one color.
That should have been stated.
Painting with 2 colors
total no. painting 5 doors with 2 colors =
now this combination will also be having case where all the doors were painted same with color...
no of such cases = 2
total no. painting 5 doors with 2 colors(choosing 2 colors of 5) =
Painting with 1 colours
so total = 305