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

The urn contains 6 balls: 1 white, 2 red, 3 black. Draw 3 balls at random. What is the probability that all the balls will be different colors?

The total number of balls is 1 + 2 + 3 = 6.
The total number of outcomes when drawing 3 balls out of 6:
(6.3) = 6! / (3! (6 – 3)!) = 4 5 6 / (1 2 3) = 20;
The number of ways to pull one white ball out of one:
C (1,1) = 1;
The number of ways to pull one red ball out of two:
C (2.1) = 2;
The number of ways to draw one black ball out of three:
C (3.1) = 3;
The number of favorable options when the balls are multi-colored:
m = C (1,1) C (2.1) C (3.1) = 1 2 3 = 6.
The probability that the balls are multi-colored:
P = m / n = 6/20 = 0.3.
The answer is 0.3.