There are 8 balls in an urn of which 2 are black 2 are red 2

There are 8 balls in an urn, of which 2 are black, 2 are red, 2 are blue, and 2 are yellow. You draw 3 balls at random from the urn without replacement. What is the probability that two of them are the same color?

Solution

P(  that two of them are the same color in 3 Drawn) = P( 2 Black & other) + P( 2 Blue & other) + P( 2 Red & other) + P( 2 Yellow & other) = 2 C 2 * 6 C 1 / 8 C 3 + 2 C 2 * 6 C 1 / 8 C 3 + 2 C 2 * 6 C 1 / 8 C 3 + 2 C 2 * 6 C 1 / 8 C 3

= 1/ 8 C 3 [ 6 + 6 + 6 + 6 ] = 24 / 8 C 3 = 24 * 3 * 2 / 8 * 7 * 6 = 0.4285