Handshakes among four couples skipping partners

Question

Eight people, forming four couples, meet. Every person shakes hands once with each other person except his or her own partner. How many handshakes take place?

Short answer

$24$ . There are $\binom82=28$ pairs of people, and the four partner pairs do not shake, leaving $28-4=24$ .

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Lessons behind this question

Counting and Combinatorics

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