Three in a shuffle

Level pending

In my MP3 player, I have 55 distinct songs, all grouped under 10 different albums, and the number of songs grouped under Album \(k\) is also \(k\) (so there is 1 song in Album 1, 2 songs in Album 2 and so on). I turn on shuffle mode and the MP3 player randomly picks and plays a song.

If the MP3 player randomly picks and plays the next 2 songs without replacement, the probability that all 3 songs are in the same album can be expressed as \(\frac{a}{b}\), where \(a\) and \(b\) are positive coprime integers. What is the value of \(a+b\)?

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