Permutations & Combinations
Tournament Matches Without Couples
nta_pyq_2023_apr
Grade 11
Question:
In a mixed doubles tournament, if matches where no couple plays together $=840$, then total participants is ________.
Step-by-Step Solution
Key Concept: $n$ couples $=2n$ players. Number of matches where no couple plays: $\binom{2n}{2}-n$ mixed pairs choose opponents... Actually matches with no couple: $n(2n-1)-n=n(2n-2)$... Total valid matches $=\binom{n}{2}\cdot2\cdot(n-2)!\cdot...$. Use formula for mixed doubles.
Total participants $=16$.
Correct Answer: 16