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There are (5 + 3) = 8 total people.

The shaker can be any one of 8 people.

The shakee can be any one of the remaining 7 people.

The total number of handshakes is (8 x 7) = 56 .

But . . .

We can't tell the difference between 'A' shaking 'B's hand, and 'B' shaking 'A's hand. For each

of the 56 possibilities, there's another one of the 56 possibilities that looks identical.

So the number of unique, distinct handshakes, with different pairs of shaker/shakee, is (56/2) = 28 .

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