Question

A city distributes vehicle identification stickers using a combination of letters followed by a combination of​ digits, each of which may be used more than once. determine the number of possible stickers under the given circumstances. ​a) using 55 letters and 33 ​digits, how many stickers are​ possible

Answer 1

First we have to answer some elementary question before answering.
How many digits numbers are there: 10 of course, they are 0, 1, ..., 9.
How many letters in the english alphabet: 26.
Each time we need a character, we have 26 possibilities (since repetitions are allowed)
the stickers contains 55 letters, so the number of possible combination of the 55 letters is:
`26^(55)`
Same thing for the 33 digits: each time 10 possibilities, resulting in
`10^(33)`
In order to get the whole number of possibilities, simply multiply the two previous found numbers like this:

`26^(55) * 10^(33) \text{ possibilities }`