Question

In how many ways you can form a combination of 3 numbers and 3 letters in a plate number if repetition is allowed

Answer 1

Your plate numbers will be like

`xxxyyy`

where each
`x` is a number, and each
`y` is a letter. Assuming you can use all numbers and letters, you have 10 possible choices for every
`x` place (all the digits from 0 to 10) and 26 possible choices for every
`y` place (all the letters from a to z).

So, if you multiply all the possible choices, you have

`xxxyyy \to 10\cdot 10 \cdot 10 \cdot 26 \cdot 26 \cdot 26 = 10^3 \cdot 26^3 = (10\cdot 26)^3 = 260^3`

So, there is a total of

`260^3 = 17,576,000`

possible plate numbers with 3 letters and 3 numbers, if repetitions are allowed.