If numbers and letters can be repeated, how many different 6 - digit license plates can be made if the first two positions are letters and the last four are digits
English letters?
27*27*10*10*10*10 This assume zero and the letter O can both be used.
Yes, English letters
Good, then you know what to change.
Well, let's see. If the first two positions are letters, we have 26 options for each position since there are 26 letters in the alphabet. So that gives us 26 * 26 = 676 different combinations for the first two positions.
Now, for the last four positions, we have 10 options for each position since there are 10 digits (0-9). So that gives us 10 * 10 * 10 * 10 = 10,000 different combinations for the last four positions.
To find the total number of different combinations, we multiply the number of combinations for the first two positions (676) by the number of combinations for the last four positions (10,000).
So in total, there can be 676 * 10,000 = 6,760,000 different 6-digit license plates. That's a lot of possibilities! Just remember not to try all of them at once when you're looking for your car.
To find the number of different 6-digit license plates that can be made if the first two positions are letters and the last four are digits, we need to consider the number of possibilities for each position.
First, let's focus on the first two positions. Since letters can be repeated, there are 26 possibilities for each position (assuming we consider all uppercase or all lowercase letters).
Therefore, the number of possibilities for the first two positions is 26 * 26 = 676.
Now, let's move to the last four positions. Since digits can be repeated, there are 10 possibilities for each position (0-9).
Therefore, the number of possibilities for the last four positions is 10 * 10 * 10 * 10 = 10,000.
To get the total number of different 6-digit license plates, we need to multiply the number of possibilities for the first two positions by the number of possibilities for the last four positions:
Total number of different license plates = 676 * 10,000 = 6,760,000.
Therefore, there are 6,760,000 different 6-digit license plates that can be made if the first two positions are letters and the last four are digits.