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There are n houses on a street numbered h1; : : : ; hn. Each house can either be painted blue or red. i. How many ways can the houses h1; : : : ; hn be painted? ii. Suppose n ≥ 4 and the houses are situated on n points on a circle. There is an additional constraint on painting the houses: exactly two houses need to be painted blue and they cannot be next to each other. How many ways can the houses h1; : : : ; hn be painted under this new constraint? iii. How will your answer to the previous question change if the houses are located on n points on a line. first part my answer is 2^n. i need help for rest 2 parts.

There are n houses on a street numbered h1; : : : ; hn. Each house can either be painted blue or red.
i. How many ways can the houses h1; : : : ; hn be painted?
ii. Suppose n ≥ 4 and the houses are situated on n points on a circle. There is an additional constraint on painting the houses: exactly two houses need to be painted blue and they cannot be next to each other. How many ways can the houses h1; : : : ; hn be painted under this new constraint?
iii. How will your answer to the previous question change if the houses are located on n points on a line.

 

first part my answer is 2^n. 

i need help for rest 2 parts. 

Grade:12th pass

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