One student will be randomly selected out of 100 as follows.
1. Each student will be assigned a number with the digits 1 through 5 allowed.
2. Several wheels with five sectors labeled 1 through 5 will be spun, and a number will be read from each wheel.
3. If the outcome matches some student's number, the student is selected.
4. If the spin produces an outcome not corresponding to any student, the wheels will be spun again until the outcome matches some student.
What is the minimum number of wheels that will allow each student to be encoded with a unique outcome?
A. 2
B. 3
C.15
D.20
To determine the minimum number of wheels required to encode each student with a unique outcome, we need to consider the number of possible combinations that can be generated by spinning the wheels.
In this scenario, each wheel has 5 sectors labeled 1 through 5. Therefore, there are 5 possible outcomes for each wheel.
To calculate the total number of combinations, we multiply the number of sectors on each wheel by each other. Since we have a fixed number of wheels, we can express this as:
Total combinations = (Number of sectors on each wheel) ^ (Number of wheels)
Initially, we have 100 students. In order to encode each student with a unique outcome, we require the total number of combinations to be equal to or greater than 100.
Now, let's calculate the minimum number of wheels required. We can start with the given options:
A. 2 wheels: (5^2) = 25 combinations, which is less than 100.
B. 3 wheels: (5^3) = 125 combinations, which is greater than 100.
Therefore, the minimum number of wheels that allows each student to be encoded with a unique outcome is 3.
The correct answer is B. 3.
5 * 5 = 25
5 * 5 * 5 = 125