If two distinct members of the set {2, 4, 10, 12, 15, 20, 50} are randomly selected and multiplied, what is the probability that the product is a multiple of 100? Express your answer as a common fraction.
There are 7 nCr 2 = 21 outcomes for the 7 numbers in the set and they are as follows:
(8, 20, 24, 30, 40, 100, 40, 48, 60, 80, 200, 120, 150, 200, 500, 180, 240, 600, 300, 750, 1000) = 21
There are 7 multiples of 100 (including 100 itself). Therefore, the probability would be:
7 / 21 = 1/3
