Rock On Probability

Probability 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 $a+b$ .

The answer is 463.

1 solution

Satyen Nabar
Jun 4, 2015

Since there are $6$ Pink Floyd songs, they have to occupy odd-numbered positions. There are $6$ choices for first song, $5$ choices for third song, $4$ choices for fifth song and so on.

There are $5$ choices for second song from any of the U2 and Deep Purple numbers, $4$ choices for the fourth song and so on.

So that's a total of $6*5*4*3*2*1*5*4*3*2*1= 86400$ ways.

The total number of ways is $11! = 39,916,800$ ways.

Answer is $\dfrac{1}{462}$ , so $1+462=463$

So you are back? :) It seemed like you had gone inactive for a while . Earlier there were a lot of questions by you , but you haven't posted questions in a while .

Anyway, correct me if I am wrong .

A Former Brilliant Member - 6 years ago

Yes was out on vacation Azhaghu. But am back n hopefully twice as active :)

Satyen Nabar - 6 years ago

Good to have you back :D

A Former Brilliant Member - 6 years ago

Great problem and solved it the same way - not so great bands though :)

Lawrence Mayne - 5 years, 7 months ago

Hey . Did you just forget the fact that a C.D. plays songs in a circular loop and not in a straight line ????

ANIL GOYAL - 1 year, 7 months ago

So it should be 10! in the denominator instead of 11! . This gives us the answer 43 .

ANIL GOYAL - 1 year, 7 months ago

Rock On Probability

The answer is 463.

1 solution

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