Question

A box contains 40 balls: 10 white, 25 black and 5 red balls. Three balls are extracted
from this box. What is the probability that the three balls are of different colors?

Answer 1

P(all white) = 10/40 * 9/39 * 8/38
P(all black) = 25/40 * 24/39 * 23/38
P(all red) = 5/40 * 4/39 * 3/38
P(all the same) is the sum of those three
P(not all one color) = 1 - P(all the same)

Answer 2

or
C(10,1) * C(25,1) * C(5,1) / C(40,3)
= 125/988

oobleck forgot to subtract all cases of something like RRB,
that is, 2 of one colour, 1 other, giving you cases of only 2 colours