Question

a states license plates consist of 3 letters followed by 3 numbers. what is the probability of randomly generating a license plate that reads ahw 304? (1 point) 11,232,000 1/11,232,000 1/17,576,000 17,576,000

Explanation:

Step1: Calculate the total number of possible license - plate combinations

There are 26 letters in the alphabet. For the 3 - letter part, the number of ways to choose the first letter is 26, the second letter is 26, and the third letter is 26. So the number of ways to choose the 3 - letter combination is \(26\times26\times26=26^{3}\).
There are 10 digits (0 - 9). For the 3 - number part, the number of ways to choose the first number is 10, the second number is 10, and the third number is 10. So the number of ways to choose the 3 - number combination is \(10\times10\times10 = 10^{3}\).
The total number of license - plate combinations \(N=26^{3}\times10^{3}\).
Since \(26^{3}=26\times26\times26=17576\) and \(10^{3}=1000\), then \(N = 17576\times1000=17576000\).

Step2: Calculate the probability

The probability \(P\) of getting a specific license plate (in this case, AHW304) is given by the formula \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\).
The number of favorable outcomes is 1 (since we want only one specific license plate: AHW304).
So \(P=\frac{1}{17576000}\)

Answer:

\(\frac{1}{17576000}\) (the third option)