1Thank you for the explanation:)
P.S. your last observation wasn't quite as unique as the rest of it=P
In a series of games between team A and team B,they decide to play on till a team wins 5 matches .In how many ways can A win the series if no match ends in a draw?
Please explain how you solved it!
Answer is 126
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3 Answers
21Hint :
If A is to win , then there can at most be 9 match and in the last match A must win since after that the game stops. (If there are 10 or more than 10 games, then B must already have won 5 games, so A can't win, in fact in this sort of series at most 9 games can be played ... )
So if A finishes the series by winning the 9-th game , then A will have to win some 4 of the remaining 8 games. which can happen in C(8,4) ways.
and if A finishes the series by winning the 8-th game , then A will have to win some 4 of the remaining 8 games. which can happen in C(7,4) ways.
and if A finishes the series by winning the 7-th game , then A will have to win some 4 of the remaining 8 games. which can happen in C(6,4) ways.
and if A finishes the series by winning the 6-th game , then A will have to win some 4 of the remaining 8 games. which can happen in C(5,4) ways.
and if A finishes the series by winning the 5-th game , then A will have to win some 4 of the remaining 8 games. which can happen in C(4,4) ways.
Since all those cases can't overlap (mutually exclusive), in order to find total number of ways, we just need to add them
So total number of ways = C(8,4) + C(7,4) + C(6,4) + C(5,4) + C(4,4) = 70 + 35 + 15 + 5 + 1 = 126
PS: I'm being reminded of Shampoo
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