Question

Suppose that one state’s license plates consist of 1 digit followed by 4 letters followed by 2 digits. How many such plates can the state issue?

Answer 1

The state can issue 456,976,000 license plates.

Explanation:

For digits, it is assumed that we can use 0-9. Thus, there are 10 options for each slot with a digit.

For letters, it is assumed that we can use the 26 letters of the alphabet (i.e. A through Z). Thus, there are 26 options for each slot with a letter.

For this particular problem, the slot method can be used. Assuming that repetition of letters/digits is allowed:

`\frac{10}`
`\frac{26}`
`\frac{26}`
`\frac{26}`
`\frac{26}`
`\frac{10}`
`\frac{10}`

= 10*26*26*26*26*10*10

=456,976,000.

Therefore, the state can issue 456,976,000 license plates.