S 2 Cs Pankaj and Prateek play a unigue game series in a chess tournament They decide to play on till one of them wins 5 matches. If each match end only in win or loss. Nunmber of ways in which series can be won by either of them, is
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Step-by-step explanation:
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 :
WWW
So, answer
=1+
4!1!
5!
+
4!2!
6!
+
4!3!
7!
+
4!4!
8!
=1+5+15+35+70
=126
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