How many 4-digit license plates can be made by using the digits 0, 2, 4, 6, and 8 if repetitions are allowed? if
repetitions are not allowed?
repetitions allowed: 5^4 = 625
no repetions allowed: 5x4x3x2= 120
To find the number of 4-digit license plates that can be made using the digits 0, 2, 4, 6, and 8, we need to consider two cases: one where repetitions are allowed and one where repetitions are not allowed.
Case 1: Repetitions are allowed
In this case, we have 5 options for each digit (0, 2, 4, 6, and 8), and we need to choose 4 digits for the license plate. Since repetitions are allowed, we can choose any digit for each position. Therefore, the total number of possibilities is given by 5^4.
Number of 4-digit license plates with repetitions allowed = 5^4 = 625
Case 2: Repetitions are not allowed
In this case, we still have 5 options for the first digit. However, for the second digit, we have only 4 options left (as we can't repeat the digit we used for the first digit). Similarly, for the third digit, we have 3 options left, and for the fourth digit, we have 2 options left.
Number of 4-digit license plates with repetitions not allowed = 5 * 4 * 3 * 2 = 120
Therefore, there can be 625 different 4-digit license plates if repetitions are allowed, and 120 different 4-digit license plates if repetitions are not allowed.