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Sagot :
Using the Fundamental Counting Theorem, it is found that the number of possible ZIP codes is:
[tex]9^9 =387,420,489[/tex]
Fundamental counting theorem:
States that if there are n things, each with [tex]n_1, n_2, …, 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:
- The first digit cannot be 3, hence there are 9 possible outcomes for the first digit, that is, [tex]n_1 = 9[/tex].
- For the next 8 digits, there are also 9 possible outcomes, as it cannot repeated the previous digit, hence [tex]n_2 = n_3 \cdots n_9 = 9[/tex]
Hence:
[tex]N = n_1 \times n_2 \times \cdots \times n_9 = 9^9 = 387,420,489[/tex]
A similar problem is given at https://brainly.com/question/19022577
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