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We have to design colour code for all books in our class.we are going to have 4 straight stripes on each book. We could colour each stripe in one of six colours. it didn't matter if more than one stripe had the same colour, not even if they were adjacent. but we can't have all the stripes the same colour.how many different book we code in this way?
My answer is 1080 but book ans. Is different.....plese help me
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You can color the first strip in any of 6 colors. It gives you 6 options.
You can color the second strip in any of 6 colors. It gives you 6 options.
Third strip - 6 options.
Fourth strip - 6 options.
In total, there are = 1296 options, so far.
Now, take off the cases when all 4 strips are colored in one of 6 colors, i.e. 6 options.
Thus you have 1296 - 6 = 1290 options.