A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?
Choose the correct choice from the following choices.
A) 1/6
B) 7/216
C) 1/36
D) 9/216
E) 11/216
the total number of possible outcomes is, of course, 6^3.   Fortunately, there are only two combinations of three dice throws that will give you a sum of 16:   5, 5, 6   4, 6, 6   (I have a hard time remembering a real GMAT question that would give you 12, as the number of potential combinations is indeed inordinately large and difficult to map out.)   However, our denominator counts out the number of throwing sequences (permutations) and not just combinations, so we will need to do the same. Effectively there are three throwing sequences for either combination:   6, 5, 5   5, 6, 5   5, 5, 6   4, 6, 6   6, 4, 6   6, 6, 4   So 6 throwing sequences we want divided by 6^3 throwing sequences we could get gives us 1/(6^2) or 1/36.   ANSWER:1/36
<result>C</result>
A fair sided die labeled 1 to 6 is tossed three times. What is the probability the sum of the 3 throws is 16?