MathCastle
Counting & ProbabilityHardExpected Value, Linearity & Advanced Probability

Expected Value, Linearity & Advanced Probability · Hard problem

The numbers 1,2,…,71,2,\dots,7 are placed in a row in uniformly random order. Find the expected number of adjacent pairs whose two values are consecutive integers (differ by exactly 11).

The answer is a fraction mn\tfrac{m}{n} in lowest terms; find m+nm + n.