Rock On Probability

Discrete Mathematics Level 4

I burned a CD today with Rock numbers by a few of my favorite bands. The list of songs is as follows.

\((1)\) With or without you -- U2

\((2)\) Where the streets have no name - - U2

\((3)\) Still haven't found what I'm looking for - - U2

\((4)\) Another brick in the wall - - Pink Floyd

\((5)\) Comfortably numb- - Pink Floyd

\((6)\) Brain Damage - - Pink Floyd

\((7)\) Time - - Pink Floyd

\((8)\) Wish you were here - - Pink Floyd

\((9)\) Hey You - - Pink Floyd

\((10)\) Smoke on the water - - Deep Purple

\((11)\) Highway Star - - Deep Purple.

While listening to these epic numbers, I put my CD player on random i.e the tracks were played in no set order.

If the CD player plays through all \(11\) tracks without repeating any of them, the probability that no two songs by the same band will be played one after the other is given by \(\dfrac{a}{b}\) where \(a\) and \(b\) are co-prime positive integers.

Find \(a+b\).


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