Using the Fundamental Counting Theorem, it is found that 1,835,008 numbers are possible.
What is the Fundamental Counting Theorem?
It is a theorem that 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, we have that:
- For the first digit, there are 7 possible outcomes, hence [tex]n_1 = 7[/tex].
- For the remaining 6 digits, there are 8 possible outcomes, hence [tex]n_2 = \cdots = n_7 = 8[/tex].
Hence:
N = 7 x 8 x 8 x 8 x 8 x 8 x 8 = 1,835,008.
1,835,008 numbers are possible.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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