Using the Fundamental Counting Theorem, it is found that there are 10 positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1.
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]
The number of options for each selection are given as follows, considering there are 10 possible digits, and that the last two are fixed at 7 and 1, respectively:
[tex]n_1 = 10, n_2 = n_3 = 1[/tex]
Hence, the number of integers is given by:
N = 10 x 1 x 1 = 10.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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