Answer:The probability of arranging 5 out of 12 CDs in alphabetical order by chance is 1/95,040, calculated based on permutations to determine total arrangement possibilities.
Step-by-step explanation:
The question asks: You own 12 CDs. You want to randomly arrange 5 of them in a CD rack. What is the probability that the rack ends up in alphabetical order? To solve this, first understand that only one specific arrangement of the five CDs will be in alphabetical order. The total number of ways to arrange 5 CDs out of 12 is a permutations problem, which can be calculated using the formula for permutations: P(n,r) = n! / (n-r)!, where n is the total number of items, and r is the number of items to arrange.In this case, n=12 (total CDs) and r=5 (CDs to arrange), so P(12,5) = 12! / (12-5)! = 12! / 7! = 95,040 ways. Since there is only one alphabetical arrangement out of these, the probability is 1/95,040. This represents the chance of randomly arranging 5 out of 12 CDs in a specific order.
