Question

How many positive three-digit integers have the hundreds digit equal to 7 and the units (ones) digit equal to 1?

Answer 1

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.

What is the Fundamental Counting Theorem?

It is a theorem that 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:

$N = n_1 \times n_2 \times \cdots \times n_n$

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:

$n_1 = 10, n_2 = n_3 = 1$

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 brainly.com/question/24314866

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