Question

in california, each automobile license plate consists of a single digit followed by three letters, followed by three digits. how many distinct license plates can be formed if there are no restrictions on the digits or letters? (do not use any spaces or commas in your answer)

Explanation:

Step1: Determine number of choices for each position

There are 10 choices (0 - 9) for each digit position and 26 choices (A - Z) for each letter position.

Step2: Apply multiplication principle

The license - plate has 1 digit, then 3 letters, then 3 digits. The total number of license plates is the product of the number of choices for each position.
The number of ways to choose the first digit is 10. The number of ways to choose the three letters is \(26\times26\times26=26^{3}\). The number of ways to choose the last three digits is \(10\times10\times10 = 10^{3}\).
The total number of license plates \(N=10\times26^{3}\times10^{3}\).
\[

$$\begin{align*} N&=10\times(26\times26\times26)\times(10\times10\times10)\\ &=10\times17576\times1000\\ &=175760000 \end{align*}$$

\]

Answer:

175760000