If a license plate uses a three-digit number followed by three letters of the english alphabet, how many license plates can be made?

There are 17,576,000 different possibilities.

The problem doesn't state that the numbers can't be repeated. Therefore, we will assume that numbers and letters can be repeated.

To find the solution, we just need to multiply the number of possibilities for each position.

10 x 10 x 10 x 26 x 26 x 26

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1rstar 1rstar · Answer 2 · 2018-04-15T18:07:46+02:00

[tex]PERMUTATIONS \: \: AND \: \: \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: COMBINATIONS \\ \\ \\ We've \: to \: create \: a \: license \: plate \: \\ using \: \: 3 \: \: numbers \: and \: \: 3 \: \: alphabets \\ \\
As \: we \: know \: , \: there \: are \: 10 \: choices \\ for \: selection \: of \: the \: numbers \: i.e. \: \\ from \: \: 0-9
\\ \\ Aslike \: for \: the \: alphabets \: we've \: \\ got \: 26 \: choices \: that \: is \: A-Z \\ \\ \\ Since \: repeatation \: of \: letters \: and \: \\ numbers \: isn't \: restricted \: , \\ \\ Number \: of \: license \: plates \: that \: \\ can \: be \: made \: \\ = 10 \times 10 \times 10 \times 26 \times 26 \times 26 \\ \\ \\ = \: 17576 \: \: \: \: \: \: \: \: \: \: Ans.[/tex]