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
Create a free account to view solution
View Solution FreeMore Permutation and Combination Questions
How many numbers can be formed with the digits 2,3,5,7,0 which are greater than 70,000 (Rept. not allowed) ?...Eleven animals of a circus have to be placed in eleven cages, one in each cage. If four of the cages are too small for s...If 4 parallel lines intersect another set of 3 parallel lines, then number of parallelograms formed with these lines is-...The number of ways in which n distinct things can be put into two different boxes so that no box remains empty, is-...The number of words which can be formed from the letters of the word ′BHARATPUR′ so that P,U,R always remain...