Permutation and CombinationHard
Question
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:
Options
A.126
B.252
C.225
D.none
Solution
Case - I when all 5 match win the india then total
no. of ways = 5C5
Case - II when 6th match win the india then total
no. of ways = 5C4
Case - III when 7th match win the india then total
no. of ways = 6C4
Case - IV when 8th match win the india then total
no. of ways = 7C4
Case - V when 9th match win the india then total
no. of ways = 8C4
Hence required no. of ways
= 1 + 5 + 6C4 + 7C4 + 8C4
= 1 + 5 + 15 + 35 + 70 = 126
no. of ways = 5C5
Case - II when 6th match win the india then total
no. of ways = 5C4
Case - III when 7th match win the india then total
no. of ways = 6C4
Case - IV when 8th match win the india then total
no. of ways = 7C4
Case - V when 9th match win the india then total
no. of ways = 8C4
Hence required no. of ways
= 1 + 5 + 6C4 + 7C4 + 8C4
= 1 + 5 + 15 + 35 + 70 = 126
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