Question

License plates in a particular state display 3 letters followed by 3 numbers. How many different license plates can be manufactured? (Repetitions are allowed.)

Answer 1

Using the fundamental counting theorem, it is found that 17,576,000 different license plates can be manufactured.

Fundamental counting theorem:

States that if there are n things, each with $n_1, n_2, \cdots, n_n$ ways to be done, each thing independent of the other, the number of ways they can be done is:

$N = n_1 \times n_2 \times \cdots \times n_n$

In this problem:

• Since repetition is allowed, for the 3 letters, there are 26 outcomes, hence $n_1 = n_2 = n_3 = 26$.

• For the 3 numbers, there are 10 outcomes, hence $n_4 = n_5 = n_6 = 10$

Then:

$N = 26^3 \times 10^3 = 17576000$

17,576,000 different license plates can be manufactured.

To learn more about the fundamental counting theorem, you can take a look at brainly.com/question/24314866