Permitted
Probability
Level
1
A new flag has to be designed with 6 vertical strips using some or all of the colours yellow,green,blue and red.In how many ways can this be done so that no two adjacent stripes have the same colour?
The answer is 972.
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1 solution
There are 4 ways to choose color for the first strip.
There are 3 ways to choose color for the second strip (other the first strip's color) .
There are 3 ways to choose color for the third strip (other the second strip's color) .
There are 3 ways to choose color for the fourth strip (other the third strip's color) .
There are 3 ways to choose color for the fifth strip (other the fourth strip's color) .
There are 3 ways to choose color for the sixth strip (other the fifth strip's color) .
So, there are 4 . 3 . 3 . 3 . 3 . 3 = 9 7 2 ways to design this flag.