Question

License plates are made using 3 letters followed by 2 digits. How many plates can be made if repetition of letters and digits are allowed?

Answer 1

We need to determine the number of different license plates for the specified situation possible in this issue. They also claimed in the issue that the plate consists of 3 letters followed by 2 digits. But first, we're going to determine the number of options to pick 3 letters from the 26 letters we have. We can now determine the number of options to pick 2 digits, which is 10, from the number of digits we have. After that multiply, the number of ways obtained to get the desired result.

Complete step by step answer:
It is given that a license plate is composed of 3 letters and 2 digits.
First considering the letters on the plate.
The plate is made up of 3 letters. We've got 26 characters, starting from A to Z. So, we can pick 3 letters from 26 letters in ${26^3}$ ways.
Now, considering the numbers on the plate.
The plate is made up of 2 digits. We've got 10 digits, starting from 0 to 9. So, we can pick 2 digits from 10 digits in ${10^2}$ ways.
So, the possible ways are,
$\Rightarrow {26^3} \times {10^2} = 1757600$

Hence, the number of different plates will be 1757600.

Note: We can see that the letters and numbers on the number plates are repeated, so the reputation was considered. If they have specified that the picture is not permissible in the problem, then we will go to the idea of permutations and combinations.
A permutation is when, in some particular order or sequence, you organize a series of results. Also, you can rearrange them by using permutation formulas if the data is already ordered in sequence. Permutation occurs in most fields of mathematics.
Unlike permutation, a combination is when, without any order or sequence, you select data from a group. If the data group is comparatively smaller, you can measure the number of variations available.