Question

how many ways are there to paint the 10 identical rooms in a hotel with five colors if at most three rooms can be painted green, at most three painted blue, at most three red, and no constraint is laid on the other two colors, black and white?

Answer 1

Using the Combination formula,

Total number of ways there to paint 10 hotel rooms in a hotel with five colours is 527 ways .

We have given that,

total number of rooms available for paint = 10

number of colour avaliabile for painting = 5

Atmost three rooms can be painted green i.e

the number of ways for atmost three rooms are painted green = ¹⁰C₃ + ¹⁰C₂ + ¹⁰C₁ = 120 + 45 + 10 = 175

similarly, the number of ways for atmost three rooms are painted red = 175

the number of ways for atmost three rooms are painted blue = 175

Now, one room is remained for painting and two colours are available for it

the number of painting the remained room with aany of two available colours i.e black and white

= 2 ways

thus , total ways to paint the 10 hotel rooms with five different paints are (175×3 +2) = 527

To learn more about Combination formula, refer:

https://brainly.com/question/16837159

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