how many two digit numbers can be made using only these digits 2,4,6,8
show work and explain
essentially what you are asking is how many ways to arrange 4 unique digits.
P(4,4) = 4! = 24
i meant different before 2 sorry
To determine the number of two-digit numbers that can be made using the digits 2, 4, 6, and 8, we need to consider two scenarios:
Scenario 1: The first digit can be any of the given digits (2, 4, 6, or 8), and the second digit can also be any of the given digits (2, 4, 6, or 8). This allows for a repetition of digits.
To calculate the number of possibilities for each digit position (first and second), we can multiply the number of options available for each position. In this case, there are four options for each digit position since there are four given digits (2, 4, 6, and 8). Therefore, the total number of possibilities for this scenario can be calculated as follows:
Total possibilities (Scenario 1) = Number of options for the first digit position * Number of options for the second digit position
Total possibilities (Scenario 1) = 4 * 4 = 16
So, there are 16 possible two-digit numbers that can be formed by using the digits 2, 4, 6, and 8, allowing for repetition.
Scenario 2: The first digit can also be any of the four given digits (2, 4, 6, or 8), but the second digit cannot be the same as the first digit (non-repetitive).
To calculate the number of possibilities for each digit position in this scenario, we need to consider two cases:
Case 1: The first digit is a given digit (2, 4, 6, or 8). In this case, there are four possible options for the first digit position.
Case 2: The second digit cannot be the same as the first digit. In this case, there are three possible options for the second digit position since one option (the first digit) is already used.
To calculate the total possibilities for this scenario, we multiply the number of options available for each digit position:
Total possibilities (Scenario 2) = Number of options for the first digit position * Number of options for the second digit position
Total possibilities (Scenario 2) = 4 * 3 = 12
So, there are 12 possible two-digit numbers that can be formed by using the digits 2, 4, 6, and 8 without repetition.
To find the overall total number of two-digit numbers that can be formed, we add the possibilities from Scenario 1 and Scenario 2:
Overall total possibilities = Total possibilities (Scenario 1) + Total possibilities (Scenario 2)
Overall total possibilities = 16 + 12 = 28
Therefore, there are a total of 28 possible two-digit numbers that can be made using only the digits 2, 4, 6, and 8.