Question 867478
There are {{{24*24}}} or {{{576}}} possible outcomes.
There are {{{16}}} sums of {{{17}}}. (1,16) (2,15), ...., (15,2), (16,1)
There are {{{24+23}}} or {{{47}}} one for each (5,X) pair and one for each (Y,5) pair (not including Y=5).  
So,
{{{P=1/576+47/576=48/576=1/12}}}