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805+ (Hard)|   Combinations|      
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Bunuel
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In a unique hockey series between India & Pakistan, they decide to pla 18 Feb 2021, 03:15
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45% (02:38) correct 55% (02:27) wrong based on 104 sessions

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In a unique hockey series between India & Pakistan, they decide to play on till a team wins 5 matches. The number of ways in which the series can be won by India, if no match ends in a draw is:

(A) 126
(B) 225
(C) 252
(D) 277
(Е) 302


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Neha2404
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In a unique hockey series between India & Pakistan, they decide to pla 18 Feb 2021, 04:43
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IMO-A
Maximum possible match between india and pakisthan is -9
To won the series india need to won 5 match and pakisthan can won 4 matches
No of possible ways to won the series by india is =9C5
=9*8*7*6*5/5!
=126

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Gayu1994
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In a unique hockey series between India & Pakistan, they decide to pla 18 Feb 2021, 04:20
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How do we do this question without knowing the max number of games they play against each other ?

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ShaikhMoice
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In a unique hockey series between India & Pakistan, they decide to pla 21 Jun 2021, 07:06
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Neha2404
IMO-A
Maximum possible match between india and pakisthan is -9
To won the series india need to won 5 match and pakisthan can won 4 matches
No of possible ways to won the series by india is =9C5
=9*8*7*6*5/5!
=126

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But why are we not considering the cases where India wins all 5 matches in a row , 5 win for india 1 for pakistan , 5 india 2 pakistan or 5 india 3 pakistan
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rollinbusiness
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In a unique hockey series between India & Pakistan, they decide to pla 08 Feb 2023, 09:01
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Shaik

I thought the same but regardless of how many games are played, India wins 5... I'm not really sure why the shortcut works tbh though...



The way I did it took way longer than 2 minutes but I got the same answer:


First off 5 games is I,I,I,I,I = 1 ways

for 6 games we know that India wins the final game so we have 5 positions where India must only win 4. So we can use the Mississippi formula for 5 positions with 4 Is and 1 P (4 alike elements and 1 alike element). Therefore 5!/4!1!.


Applying the same formula we get:

5 games = 1 way
6 games = 5 ways
7 games = 15 ways
8 games = 35 ways
9 games = 70 ways

Total =1+5+15+35+70 = 126
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In a unique hockey series between India & Pakistan, they decide to pla 17 Sep 2024, 02:29
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