General Studies I
There are two identical red, two identical black and two identical white balls. In how many different ways can the balls be placed in the cells (each cell to contain one ball) shown above such that balls of the same colour do not occupy any two consecutive cells?
Out of 3 colour, one colour (of which two balls are to be arranged) can be selected in = ways = 3 ways Two balls of same colour and two balls of different colour can be arranged together in which no two ball of same colour are adjacent = 6 ways
∴ Total number of arrangements = 6 × 3 = 18 ways
Case II : Two colour ort of 3 can be selected in = ways = 3 ways
Now, 2 balls of each colour can be arranged alternatively in 2 ways.
Hence 4 balls can be arranged (two of each colour) =
3 × 2 = 6 ways
The total number of arrangements = 18 + 6 = 24 ways