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in a unique hockey series between india and pakistan they decide to play on till one of them win 5 matches. the number of ways in which the series can be won by india a)126 b)252 c)225 d)none

in a unique hockey series between india and pakistan they decide to play on till one of them win 5 matches. the number of ways in which the series can be won by india
a)126
b)252
c)225
d)none
 

Grade:12th pass

3 Answers

Arun
25757 Points
5 years ago
Dear student

Let 'W' indicate that India wins and let 'L' indicate that India loses. Then, it is clear that in all the possible cases in which India wins, last match has to be won by India (as teams keep playing until any one of them wins 5 matches). So, all we have to do is permute 4 W's with 0,1,2,3 or 4 L's (The 5th W has to be in the last position and number of L's cannot exceed 4). i.e, all possible permutations of the left-hand side :
WWWW | W
WWWWL | W
WWWWLL | W
WWWWLLL | W
WWWWLLLL | W
 So, answer 
= 4!/4!0! + 5!/4!1! + 6!/4!2! + 7!/4!3! + 8!/4!4! 
= 1 + 5 + 15 + 35 + 70 
= 126
 
Regards
Arun (askIITians forum expert)
Rohit
103 Points
5 years ago
If 5 matches are won by India then IND wins the series.Let us discuss the cases Matches. IND. PAK. 6 5. 1 7. 3. 25. 2
Rohit
103 Points
5 years ago
Sorry I posted it by mistake I am rewriting the and below.Matches IND. PAK6. 5. 17. 5. 28. 5. 3. 9. 5. 4 Next case cannot be considered as this may lead to a tie between both teams.So now no. Of ways are 9C5Calculate the and will be 126.Hope this helpsREGARDS.

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