Respuesta :
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 [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
In this problem:
- For the first two letters, there is only one possible outcome, which are A and B, respectively, then [tex]n_1 = n_2 = 1[/tex].
- The third and fourth letters can be any which has not been used yet, hence A and B are disconsidered and [tex]n_3 = 24, n_4 = 23[/tex].
- For the three digits, considering that they have to be distinct, [tex]n_5 = 10, n_6 = 9, n_7 = 8[/tex]
Then:
[tex]N = 24 \times 23 \times 10 \times 9 \times 8 = 397440[/tex]
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
