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To become a contestant on a quiz show, a person must correctly order 4 rock stars by age, from youngest to oldest. The contestant knows which one is the oldest rock star, but randomly guesses at the order of the other 3 rock stars. What is the probability the contestant will get all 4 in the correct order ?

Question

To become a contestant on a quiz show, a person must correctly order 4 rock stars by age, from youngest to oldest. The contestant knows which one is the oldest rock star, but randomly guesses at the order of the other 3 rock stars. What is the probability the contestant will get all 4 in the correct order ?

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Solution

Since the contestant knows the oldest rock star, they only need to correctly order the remaining 3 rock stars. The total number of ways to arrange 3 items is 3 factorial (3!), which is 321 = 6.

Since there is only one correct order out of these 6 possible arrangements, the probability of the contestant guessing the correct order is 1/6.

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