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?
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