Question

Specialized license plates have seven permissible characters: letters, numbers, a dash (-)

and the ampersand (&). How many custom plates are available?

Answer 1

`Total = 38^7`

Explanation:

Given

`Plate\ Number = 7\ characters`

`Letters \to 26`
`\to [A- Z]`

`Numbers \to 10`
`\to [0 - 9]`

`Dash \to 1`
`\to [ - ]`

`Ampersand \to 1`
`\to [\&]`

Required

Number of possible characters

Since the order and ways of selecting each character is not selected, then it means that any of the permissible character can occupy any of the 7 available spaces, with repetition.

The total possible characters (n) is:

`n = 26 +10 + 1 + 1`

`n = 38`

Any of the 38 characters can occupy any of the 7 spaces.

Hence, the total number of character is:

`Total = n^7`

`Total = 38^7`