Chapter 13.2, Problem 21PPS

To determine

To find: The possible license plate fit this description if the first number was $0$ .

Answer to Problem 21PPS

The total number of choices is $600$ .

Explanation of Solution

Given:

The first letter of the license plate is $Q$ .

The second letter of the license plate is $M$ or an $N$ .

The third letter of the license plate was $B,P\text{ or }D$ .

Concept used:

The number of ways of arranging $n$ item in order $=n!$ .

The probability formula is used to compute the probability of an event to occur as:

  $P\left(A\right)=\frac{\text{Number of favorable outcome}}{\text{Total Number of favorable outcomes}}$ .

Calculation:

By the Fundamental Counting Principle, the number of possible outcomes in a sample space can be found by multiplying the number of possible outcomes from each stage or event.

The first letter of the license plate is $Q$ . There are $2$ choices for the second letter. There are $3$ choices for the third letter. The first number is $0$ There are $10$ choices for the second digit. There are $10$ choices for the third digit.

Therefore, the total number of choices is $1\times 2\times 3\times 1\times 10\times 10=600.$

Hence, the total number of choices is $600$ .