3 Dice Rolls

When a die is rolled 3 times, there are 6 · 6 · 6 = 216 possible outcomes. If a 1 is rolled first, then there are 10 possible outcomes for the next two digits such that the third digit is greater than the second, which is greater than the first. If a 2 is rolled first, then there are 6 possible outcomes for the next two digits where the digits increase. If a 3 is rolled first , there are 3 ways for the digits to increase, and if a 4 is rolled first, there is 1 way for digits to increase. So there are a total of 10 + 6 + 3 + 1 = 20 total outcomes. Thus the probability is $\frac { 20 }{ 216 } =\frac { 5 }{ 54 }$ .
$5+54=\boxed { 59 }$ .