The urn contains 6 balls: 1 white, 2 red, 3 black. three balls are drawn at random.

The urn contains 6 balls: 1 white, 2 red, 3 black. three balls are drawn at random. what is the probability that all balls will be of different colors.

The total number of outcomes when choosing 3 balls out of 6.
C (6,3) = 6! / (3! (6 – 3)!) = 6! / (3! 3!) = 20.
The number of ways to get one white ball from one:
C (1,1) = 1.
The number of ways to get one red ball is a ball out of two:
C (2,1) = 2.
The number of ways to get one black ball out of three:
C (3.1) = 3.
Number of favorable options:
m = C (1,1) C (2.1) C (3.1) = 1 2 3 = 6.
The probability that all balls are different colors:
P = m / n = 6/20 = 3/10 = 0.3.
Answer: 0.3.