A medium question on combinations for P2–P4, with a step-by-step solution, diagrams and the answer. Counting arrangements and choices appears in the Hua Xia Cup from the P1 and P2 first rounds to the P5 finals.
The question
Before a debate, 7 pupils greet each other: every two of them shake hands once.
How many handshakes are there?
Show the hints (2)
💡Hint 1: The 1st meets each of the other 6. How many more does the 2nd still need?
💡Hint 2: Each pair counts once: A with B is the same as B with A.
Worked solution
Have a go first, then read the solution step by step.
1.The 1st: 6; the 2nd: 5 more; … the last: none left.
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