Question

Suppose that in a certain state, all automobile license plates have four letters followed by three digits. How many license plates could begin with AB and have all letters and digits distinct

Answer 1

Using the Fundamental Counting Theorem, it is found that 397,440 different plates are possible.

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:

• For the first two letters, there is only one possible outcome, which are A and B, respectively, then $n_1 = n_2 = 1$.

• The third and fourth letters can be any which has not been used yet, hence A and B are disconsidered and $n_3 = 24, n_4 = 23$.

• For the three digits, considering that they have to be distinct, $n_5 = 10, n_6 = 9, n_7 = 8$

Then:

$N = 24 \times 23 \times 10 \times 9 \times 8 = 397440$

397,440 different plates are possible.

To learn more about the Fundamental Counting Theorem, you can take a look at https://brainly.com/question/24314866