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

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Ana Julia

Last answered:

April 02, 2020

Posted on:

April 01, 2020

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

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Viktor Mehandzhiyski

Posted on:

April 02, 2020

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