You own 10 compact discs (CDs). You want to randomly arrange 6 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? Be sure to leave your answer as a fraction in order to earn credit. There is a probability that the rack ends up in alphabetical order.

Total CDs (n) = 10

Number of selected CDs (r) = 6

Use permutation formula (because order of selection is important), P(n,r) = n!/(n-r)!

Setting values,

Total outcomes = P(10, 6) = 10!/(10-6)!

= 10!/4!

= (10*9*8*7*6*5*4*3*2*1)/(4*3*2*1)

= 10*9*8*7*6*5

= 151200

There is only one specific (alphabetical) order, so favorable outcome =1

total outcome = 151200

P(alphabetical order) = favorable outcome/total outcome = 1/ 151200

Therefore, There is a 1/151200 probability that the rack ends up in alphabetical order