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← JEE Main 2026 · 5 Apr · Shift 1
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JEE Main 2026 · 5 Apr · Shift 1, Mathematics question 22

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 ________.

Answer and worked solution

Official answer: 126

Count. A wins the last game. Before it, A has won 4 games and B has won kk, for k=0,…,4k=0,\dots,4:
∑k=04(4+kk)=1+5+15+35+70=126.\sum_{k=0}^4\binom{4+k}{k}=1+5+15+35+70=126.

Answer: 126