At the end of a match, ten players shake hands with each other once. How many handshakes will there be altogether?
- 45
- 20
- 55
- None of these
Explanation
When 10 players shake hands with each other once, we can calculate the number of handshakes as follows:
Each player shakes hands with 9 other players. Since there are 10 players, it would seem like there are 10 × 9 = 90 handshakes. However, this counts each handshake twice (once for each player involved).
To correct for this double-counting, we divide by 2:
Number of handshakes = (10 × 9) / 2
= 90 / 2
= 45
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