Question

Each of the six in squares in the strip, shown in figure, is to be coloured with anyone of $10$ different colours so that no two adjacent squares have the same colour. Find the number of ways of colouring the strip.

Answer 1

Now we are to colour the given six squares with $10$ colours, in such a manner that no two adjacent squares have same colour.

We have $10$ colours to colour the first square.

But we have $9$ colour to colour the second box as we can't use the colour which we have used in first square.

Again to colour the third square we will have $9$ colours as we can use the colour of first square but not the colour of second.

In the same manner we will have $9$ colours to colour third, fourth,....., sixth square. And in this pattern no two square will have same colour.

Total number of ways =$10\times 9\times 9\times 9\times 9\times 9=590490$.