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...
c)
...you paint
the two bedrooms in identical color?
d)
...you can only use grey and
yellow?
1 answers ( 0 marked as helpful)
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.
Best,
365 Vik