Question

Suppose a company is creating a new system of ID codes, all of

which will consists of 4 letters followed by a 4 numerical digits.
How many such codes are possible?

How many of the codes are possible

Answer 1

To calculate the total number of possible ID codes consisting of 4 letters followed by 4 numerical digits, we multiply 26^4 (the permutations for letters) by 10^4 (the permutations for numbers), yielding a total of 26^4 * 10^4 possible codes.

Step-by-step explanation:

To find out how many unique ID codes are possible with a system using 4 letters followed by 4 numerical digits, we need to calculate the total permutations for both the letters and the numbers.

For the letters, there are 26 possibilities for each letter (considering the English alphabet has 26 letters) and since repetitions are allowed, each of the 4 positions can be filled with any of the 26 letters. So, the number of permutations for the 4 letters is 26^4.

For the 4 numerical digits, there are 10 possibilities for each digit (0 through 9), which gives us 10^4 possible combinations for the numerical sequence.

The total number of unique ID codes can be found by multiplying the number of permutations of the letters by the number of permutations of the digits, resulting in 26^4 * 10^4 possible codes.