mp3 Shuffling

Discrete Mathematics Level 2

When a mp3 is on shuffle, after a song ends the mp3 player will choose a song at random and play it, the mp3 will not play the same song twice in a row.

Yan Yau has 10 distinct songs on his mp3. One day he goes on his mp3 and listens to 5 song on shuffle. The probability that all the songs he listened to are distinct can be expressed as \(\frac mn\) where \(m\) and \(n\) are positive coprime integers. Find the value of \(\left\lfloor \frac{m+n}{1000}\right\rfloor\).

Details and Assumptions

\(\left\lfloor x\right\rfloor\) is the floor function. \(\left\lfloor x\right\rfloor\) Is the largest integer not greater than \(x\). For example: \(\left\lfloor 3\right\rfloor = 3\), \(\left\lfloor 5.8\right\rfloor = \), \(\left\lfloor \pi \right\rfloor = 3\)


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