Question

Determine the number of possible serial numbers that can be formed with the following restrictions: The first two spaces must be consonants, the next three are non-zero numbers, and the last space is a vowel.

Answer 1

Step-by-step explanation

We have a total of 26 in the standard alphabet, 5 of them are vowel and the remaining 21 are consonants.

Also, we have 9 non-zero numbers.

The restrictions don't mention that we can't repeat letters or numbers, so we will assume we can repeat.

Since the first 2 spaces are consonants, we can pick each of them from 21 possibilities, so the combinations for that part are:

`21\cdot21`

The next three are the non-zero numbers, so we can pick each from 9 possibilities:

`21\cdot21\cdot9\cdot9\cdot9`

And the last is a vowel, so we can only pick from the 5 possibilities, so we have:

`21\cdot21\cdot9\cdot9\cdot9\cdot5`

These are all the possibilities, so we just need to evaluate the product:

`21\cdot21\cdot9\cdot9\cdot9\cdot5=1,607,445`

Answer

So, there are 1,607,445 possibilities.