SOLUTION: You own 17 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?

Question 375958: You own 17 CDs. You want to randomly arrange 9 of them in a CD rack. What is the probability that the rack ends up in alphabetical order?
Found 3 solutions by robertb, jim_thompson5910, Alyrian:
Answer by robertb(5830)   (Show Source): You can put this solution on YOUR website!
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Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
There are 17 P 9 = 17!/(17-9)! = 17!/8! = 17*16*15*14*13*12*11*10*9 = 8821612800 different ways to arrange 17 CDs into 9 positions

However, there is only one way to get them into alphabetical order (assuming each CD has a unique name)

So the probability that the rack ends up in alphabetical order is which is approximately 0.00000000011336 (ie it's a very small chance it's going to happen)
Answer by Alyrian(2)   (Show Source): You can put this solution on YOUR website!
You can't just assume there's one solution in all the permutations. Nor can you assume that just choosing is a solution.
The real solution here is finding all possible permutations of size 9 you can get from 17, or 17P9. Then you need to find all the possible ways a unique set of 9 things can be pulled from a total of 17, or 17C9 (because each set of 9 from 17 will have a correct alphabetical order).
Thus, the probability that your rack will end up in alphabetical order will be (17C9)/(17P9). This is 24310/8821612800.
Hope this helps!
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