Tim is participating in the following three math contests. On each contest, his score is the number of correct answers.
- The Local Area Inspirational Math Exam consists of 15 problems.
- The Further Away Regional Math League has 10 problems.
- The Distance-Optimized Math Open has 50 problems.

For every positive integer $n$, Tim knows the answer to the $n$th problems on each contest (which are pairwise distinct), if they exist; however, these answers have been randomly permuted so that he does not know which answer corresponds to which contest. Unaware of the shuffling, he competes with his modified answers. Compute the expected value of the sum of his scores on all three contests.

Let's think step by step and output the final answer within \boxed{}.
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