JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Permutations and Combinations

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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: 126

Solution

For

A

to win the series,

A

must capture the fifth win on some game numbered

k

, where

k = 5, 6, 7, 8, 9

. On that deciding game

A

wins, and among the preceding

k - 1

games

A

has won exactly

4

while

B

has won

k - 5

. The number of such orderings is

(4 k - 1)

, so the total is

(4 4) + (4 5) + (4 6) + (4 7) + (4 8) = 1 + 5 + 15 + 35 + 70

. The number of ways in which player

A

wins the series is

126

JEE Main · 2026 · 05 Apr 2026 · Shift 1 · Integer answer

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