### পরমমানের সমষ্টি

##### Score: 4 Points

For each permutation $a_1, a_2, a_3, \ldots,a_{10}$ of the integers $1,2,3,\ldots,10,$ form the sum $|a_1 - a_2| + |a_3 - a_4| + |a_5 - a_6| + |a_7 - a_8| + |a_9 - a_{10}|.$ The average value of all such sums can be written in the form $\frac pq ,$ where $p$ and $q$ are relatively prime positive integers. Find $p+q.$

Source: MAA

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