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?

Options

A. `1/24`
B. `1/6`
C. `1/4`
D. `1/3`

Answer

To find the probability that the contestant will get all 4 rock stars in the correct order, we can follow these steps:

1. **Identify the known and unknown**: The contestant knows which rock star is the oldest. Let's denote the oldest rock star as R4. The contestant has to guess the order of the other 3 rock stars, which we can denote as R1 (youngest), R2, and R3.

2. **Determine the total number of arrangements**: Since the contestant is guessing the order of the 3 remaining rock stars (R1, R2, R3), we need to find out how many different ways these 3 rock stars can be arranged. The number of arrangements of n items is given by n! (n factorial).

For 3 rock stars, the number of arrangements is:
\[ 3! = 3 \times 2 \times 1 = 6 \]

3. **Identify the correct arrangement**: Out of these 6 arrangements, there is only 1 correct arrangement where the rock stars are ordered from youngest to oldest (R1, R2, R3, R4).

4. **Calculate the probability**: The probability of an event is calculated as the number of favorable outcomes divided by the total number of possible outcomes. In this case, the number of favorable outcomes (correct arrangement) is 1, and the total number of possible outcomes (all arrangements of R1, R2, R3) is 6.

Therefore, the probability \( P \) is given by:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{1}{6} \]

5. **Conclusion**: The probability that the contestant will get all 4 rock stars in the correct order is \( \frac{1}{6} \).