Question

A person is writing a series name for a newly released product. It must have 4 letters followed by 3 digits. Letters are not case-sensitive and repeats are allowed. How many series names are possible?

Answer 1

Answer: 456,976,000

This value is slightly smaller than 457 million.

Step-by-step explanation

The letters are not case-sensitive. This means uppercase and lowercase are treated the same. Something like ABCD is the same as abcd.

We have 26 letters to pick from and 4 slots. There are 26^4 = 456976 different ways to pick the four letters where repeats are possible.

There are 10 digits spanning from 0 to 9. We have 10^3 = 1000 different sequences of 3 digits possible (repeats allowed).

Ultimately there are 456976*1000 = 456,976,000 different names possible. Some example names are abcd123 and efgh456.