Using the Fundamental Counting Theorem, the number of pairs are given as follows:
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]
For matching pairs, we have that:
- There are 2 options(blue/red).
- For the first option, there are 20 socks, and for the second, 19 socks.
Hence the number of pairs is:
N = 2 x 20 x 19 = 760.
For the non-matching pair, we have that there are 20 red and 20 blue to choose, hence the number of pairs is:
N = 20 x 20 = 400.
More can be learned about the Fundamental Counting Theorem at https://brainly.com/question/24314866
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