In recent years, a state has issued license plates using a combination of two letters of the alphabet followed by two digits, followed by another two letters of the alphabet. How many different license plates can be issued using this configuration?
26*26*10*10*26*26
Well, let's calculate that together! There are 26 letters in the alphabet, so we have 26 options for each of the two letters at the beginning and end. As for the digits, we have 10 options from 0 to 9.
So, the number of possible license plates is obtained by multiplying the number of options for each position together:
26 (options for the first letter) * 26 (options for the second letter) * 10 (options for the first digit) * 10 (options for the second digit) * 26 (options for the third letter).
Let's do the math:
26 * 26 * 10 * 10 * 26 = 1,757,600
So, there are 1,757,600 different license plates that can be issued using this configuration. That's quite a few! Just remember not to choose "LOL" because that one's already taken by yours truly!
To determine the number of different license plates that can be issued using this configuration, we can break down the problem into three parts:
1. Number of ways to select two letters of the alphabet:
Since there are 26 letters in the English alphabet, the number of ways to select two letters is given by the combination formula: C(n, r) = n! / (r! * (n - r)!), where n is the total number of items and r is the number of items to be selected. In this case, n = 26 and r = 2. Therefore, the number of ways to select two letters is C(26, 2) = 26! / (2! * (26 - 2)!) = 26! / (2! * 24!) = 26 * 25 / 2 = 325.
2. Number of ways to select two digits:
Since there are 10 digits (0-9), the number of ways to select two digits is given by C(10, 2) = 10! / (2! * (10 - 2)!) = 10! / (2! * 8!) = 10 * 9 / 2 = 45.
3. Number of ways to select two letters of the alphabet:
Just like in part 1, the number of ways to select two letters is 325.
Finally, to calculate the total number of possible license plates, we multiply the number of options for each part together:
Total number of license plates = (number of ways to select two letters) * (number of ways to select two digits) * (number of ways to select two letters)
= 325 * 45 * 325
≈ 4,440,625.
Therefore, there can be approximately 4,440,625 different license plates issued using this configuration.
To determine the number of different license plates that can be issued using this configuration, we need to calculate the total number of combinations possible for each position.
Step 1: Determine the possibilities for the first two letters:
Since there are 26 letters in the alphabet, there are 26 options for the first letter and 26 options for the second letter. Therefore, the number of possibilities for the first two letters is 26 * 26 = 676.
Step 2: Determine the possibilities for the two digits:
Since there are 10 different digits (0-9), there are 10 options for each of the two digits. Therefore, the number of possibilities for the two digits is 10 * 10 = 100.
Step 3: Determine the possibilities for the last two letters:
Similar to the first step, there are 26 options for each of the last two letters. Therefore, the number of possibilities for the last two letters is also 26 * 26 = 676.
Step 4: Calculate the total number of license plates:
To find the total number of license plates that can be issued, we multiply the number of possibilities for each position together: 676 * 100 * 676 = 45,616,000.
Thus, a total of 45,616,000 different license plates can be issued using this configuration.