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We need to find the total number of handshakes that occur when 8 people meet and each person shakes hands with every other person exactly once.

The concept we will use here is combinations. The number of ways to choose 2 people from a group of $n$ people is given by the combination formula:

$C(n, 2) = \frac{n!}{2!(n-2)!}$

For our situation, $n = 8$ .

Let's calculate the number of handshakes (or combinations of 2 people) when $n = 8$ :

$C(8, 2) = \frac{8!}{2!(8-2)!} = \frac{8 \times 7}{2 \times 1} = 28$

Thus, the total number of handshakes that occur is 28.

The total number of handshakes that occur is 28.

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