Permutations & CombinationsmediumPYQ · JEE Main · 5 Apr 2026 · Shift 1 (Morning)Free

Ways Player A Wins Best-of-Nine Series: 126 | JEE Main 2026

JEE Maths question with a full step-by-step solution.

Question
Two players AA and BB play a series of games of badminton. The player who wins 55 games first wins the series. Assuming no game ends in a draw, the number of ways in which player AA wins the series is
Solution
Answer: 126 (± 0.01)
Step 1: At most 99 games (worst case 44–44, then AA wins the 99th). By the bijection placing AA's 55 wins among 99 slots, the count is (95)\binom{9}{5}. Step 2: (95)=(94)=9⋅8⋅7⋅64⋅3⋅2⋅1=302424=126.\binom{9}{5}=\binom{9}{4}=\dfrac{9\cdot8\cdot7\cdot6}{4\cdot3\cdot2\cdot1}=\dfrac{3024}{24}=126. Correct answer: 126
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