Question

Four fair dice each with faces marked 1,2,3....6 are rolled together the probability of getting sum 16 is

Answer 1

@hartnn @ash2326 @satellite73

Answer 2

i guess we have to count
it is kind of going to suck

Answer 3

lol..that would be tedious.....

Answer 4

Yeah, I think it might be best to start at 6+6+3+1 from the most uneven distribution and see the most distributed is going to be 4+4+4+4, and just sort of go from there... Yeah, I have a feeling there's an easier way than counting it all out though.

Answer 5

i was starting from 1
if one die is a 1, then it is either some permutation of \((1,3,6,6)\) or \((1,4,5,6)\) or \((1,5,5,5)\)

Answer 6

or maybe try breaking them up in to pairs
if the total is 16 then taken two at a time it is either \((4,12),(5,11),(6,8),(7,9)\) or the reverse order
that might be easier

Answer 7

ok typo there, i meant \((6,10)\)

Answer 8

so for example, the probability one pair is 5 and the other is 11 is
\[\frac{4}{36}\times \frac{2}{36}\] the multiply by 2 because you have two pairs of dice

Answer 9

yeah i think that will make it much easier