2013 AIME I Problems/Problem 6
Problem 6
Melinda has three empty boxes and 
textbooks, three of which are mathematics textbooks. One box will hold any three of her textbooks, one will hold any four of her textbooks, and one will hold any five of her textbooks. If Melinda packs her textbooks into these boxes in random order, the probability that all three mathematics textbooks end up in the same box can be written as 
, where 
and 
are relatively prime positive integers. Find 
.
Solution
The probability that the three math textbooks wind up in the same box is equivalent to
