Question

Each of the six squares in a strip is to be coloured with any one of ten different colours, so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.

Answer 1

We can fill the 1st square in 10 ways

Rest of the squares can be filled in (10-1) ways owing to exclusion of the colour of their respective preceding square.

Hence total no. of ways = $10\times 9^5=590490$