JEE Main 2026 Apr 5 Shift 1, Mathematics Q22: Combinations

JEE Main2026Apr 5, Shift 1Mathematics

Two players A and B play a series of games of badminton. The player, who wins 5 games first, wins the series. Assuming that no game ends in a draw, the number of ways, in which player A wins the series is _______.

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Solution

If A wins the series in exactly $k$ games ( $k = 5, 6, 7, 8, 9$ ), then A must win the final ( $k$ -th) game and exactly $4$ of the first $k - 1$ games.

Count $= k = 5 \sum 9 (4 k - 1) = (4 4) + (4 5) + (4 6) + (4 7) + (4 8) = 1 + 5 + 15 + 35 + 70 = 126$ .

Equivalently, by the hockey stick identity this equals $(5 9) = 126$ .

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JEE Main 2026 Apr 5 Shift 1, Mathematics Q22: Combinations

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