A code is made up of two letters from the English alphabet followed by a twodigit number. How many codes are possible if
The letters and digits can be repeated in the same code?
26 letters, 10 digits, so
26^2 * 10^2
To calculate the total number of possible codes, we need to consider the following:
1. The number of possibilities for the first letter: There are 26 letters in the English alphabet, so there are 26 possible choices for the first letter.
2. The number of possibilities for the second letter: Since the letters can be repeated, the second letter can also be any of the 26 letters.
3. The number of possibilities for the two-digit number: Since the digits can be repeated, there are 10 possibilities for both the tens place and the units place of the two-digit number.
To find the total number of codes, we need to multiply the number of possibilities for each part:
Total number of codes = Number of possibilities for the first letter * Number of possibilities for the second letter * Number of possibilities for the two-digit number
Total number of codes = 26 * 26 * 10 * 10
Therefore, there are 67,600 possible codes if the letters and digits can be repeated in the same code.
To determine the number of possible codes, we need to calculate the total number of options for each part of the code and then multiply the results together.
For the first part, we have two letters from the English alphabet. Since the letters can be repeated in the same code, there are 26 options for each letter. Therefore, the total number of options for the first part is 26 * 26 = 676.
For the second part, we have a two-digit number. Since the digits can also be repeated in the same code, there are 10 options for each digit (0-9). Therefore, the total number of options for the second part is 10 * 10 = 100.
To find the total number of possible codes, we multiply the number of options for each part together: 676 * 100 = 67,600.
So, there are 67,600 possible codes if the letters and digits can be repeated in the same code.