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Bunuel
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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

Posted from my mobile device


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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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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