Question

You pick two orange balls and two green balls from a bag. You then randomly scramble them and put them in a line. What is the probability that orange and green balls won't mix (e.g. two organ balls followed by two green balls or the other way around)?

Answer 1

Number of ways in which 4 balls can be arranged = 4!

But if some are identical, we need to divide 4! by factorial of number of identical balls

Number of ways in which 2 orange balls are 2 green balls can be arranged = 4!/(2!x2!) = 6

Number of ways in which balls can be arranged such that two oranges are together and 2 greens are together = 2!

= 2       (OOGG, GGOO)

P(orange and green balls won't mix) = Number of ways in which balls can be arranged such that two oranges are together and 2 greens are together / Number of ways in which 2 orange balls are 2 green balls can be arranged

= 2/6

= 1/3