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26 December, 16:46

A circle has been split into 8 sectors each of which can be colored as 4 different colors, and no consecutive sectors are colored the same. How many ways of coloring are possible?

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  1. 26 December, 19:59
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    5832 ways

    Step-by-step explanation:

    Since the circle has 8 sectors and there is 4 colour,

    Assuming the sectors are numbered 1 to 8,

    Sector 1 : can be coloured with any of the 4 colour in 4 ways

    Sector 2 can be coloured with any of the remaining 3 colours in 3 ways

    Sector 3 in 3 ways without using the colour in sector 2

    Sector 4 in 3 ways without using the colour in sector 3

    Sector 5 in 3 ways without using the colour in sector 4

    Sector 6 in 3 ways without using the colour in sector 5

    Sector 7 in 3 ways without using the colour in sector 6

    Sector 8 in 2 ways without using the colours in sector 1 and 7

    Number of ways of colouring = 4*3*3*3*3*3*3*2 = 5832 ways
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