Two different 2-digit numbers are randomly chosen and multiplied together. What is the probability that the resulting product is a multiple of 5?
+128473 We have 90 *89 possible outcomes (some are the same) = 8010 possible outcomes
The two-digit multiples of 5 are
10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 = 18 total
The only way to get a multiple of 5 is either
!) choose one of these multiples of 5 and any other two-digit number that isn't a multiple of 5 =
(18) ( 89 - 17 ) = (18) (72) = 1296 possibilities
2) choose any two of the multiples of 5 = C(18,2) = 153 possibilities
So...the probability of a multiple of 5 is ( 1296+ 153) / 8010 ≈ .18 = 18%
