Question

question 1 of 6
a standard-issue 2020 new jersey license plate had one letter, then two digits, followed by three letters.
these plates were not allowed to have letters d, t, or x in the fourth position, or the letters i, o, or q in any position.
with these restrictions, how many different license plates were possible in 2020?

Explanation:

Step1: Calculate the number of choices for the first letter

There are 26 letters in the alphabet. Since we cannot use I, O, or Q, there are \(26 - 3=23\) choices for the first letter.

Step2: Calculate the number of choices for the two - digit part

There are 10 digits (0 - 9). So, for the two - digit part (second and third positions), the number of choices is \(10\times10 = 100\) (by the multiplication principle: for each digit position, there are 10 options).

Step3: Calculate the number of choices for the fourth letter

We cannot use D, T, X, I, O, Q. So there are \(26-(3 + 3)=20\) choices for the fourth letter.

Step4: Calculate the number of choices for the fifth and sixth letters

Since we cannot use I, O, or Q, there are \(26 - 3=23\) choices for each of the fifth and sixth letters.

Step5: Calculate the total number of license plates

By the multiplication principle \(N=23\times100\times20\times23\times23\)

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Answer:

\(24334000\)