# Permuted Problem Sets

**Discrete Mathematics**Level 4

Calvin had prepared the problem sets for Levels 1 to 5 of Geometry and Combinatorics for next week but forgot to label which set was for which level. Since Calvin didn't label them, the computer assigned them labels 1 through 5 randomly, with each label appearing only once. The probability that the problem sets given to each level are within one level of what they were supposed to be can be expressed as \( \frac {a}{b}\), where \(a\) and \(b\) are positive, coprime numbers. What is the value of \(a+b\)?

**Details and assumptions**

The computer randomly assigns each problem set to a level, and each level has exactly 1 problem set that is assigned. For example, the computer could assign the Level 1 problem set to Level 5 students, the Level 2 problem set to Level 4 students, the Level 3 problem set to Level 3 students, the Level 4 problem set to Level 2 students and the Level 5 problem set to Level 1 students.

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