Question

Helen has some black tiles, some white tiles and some grey tiles. She places a single row of
8 tiles above her washbasin. Each tile she places is equally likely to be black, white or grey.
Find the probability that there are no tiles of the same color next to each other.

Please explain what the question is trying to say and give explanation for answer

Answer 1

Start by placing the first tile, it could be any of the 3 colours.
3
now, whatever colour you placed first , the second one has to be <b>one of the other two</b>, so
3*2
for the third, it has to be <b>one of the other two colours</b> again, even the one you placed first, so
3*2*2
etc for
3*2*2*2*2*2*2*2 = 3*2^7 = 384
If we had no restrictions, the number of ways would be 3*3*3*3*3*3*3*3
= 3^8 = 6591

Prob(your event) = 384/6591 = 128/2197