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Problem 3 – c) and d) in the Additional Exercises Combinatorics

Problem 3 – c) and d) in the Additional Exercises Combinatorics


I didn`t understand the solution for the exercise 3-c) and d)

You are renovating your entire apartment and want to repaint the walls of each room. The flat
consists of two bedrooms, a kitchen, a living room, a bathroom
, a study
and a
hall, or 7 rooms in
total. You have at your disposal se
veral colors of paint: white, yellow, orange, red, purple, blue,
green, grey and pink.
How many different ways can you paint the house, assuming…
…you paint
the two bedrooms in identical color?
…you can only use grey and


1 Answer

365 Team

Hey Ana,
Thanks for reaching out!
c) So, if we paint the two bedrooms in the same color, we only need to choose 6 colors instead of 7. Hence, it’s like we have 1 fewer room, so we use variations and calculate the ways to dedicate 6 of the 9 colors to the different rooms. 
d) If we can only use 2 colors and we have 7 rooms to paint, then we’re surely repeating colors. Hence, we need to use variations with repetition, so we reach the 2^7 solution. Another way to think about this is that for every room we have two choices – we have 2 choices for the first bedroom, for each of those we have two choices for the other bedroom, then for each of those 4 choices we have two choices for the kitchen and so on. 
365 Vik

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