Question

In a unique hockey series between India and Pakistan, they decide to play on till a team wins 5 matches, The number of ways in which the series can be won if no match ends in a draw is-

• A. 126
• B. 252
• C. 225
• D. None

Answer 1

Answer: (B)

252

Answer 2

Only five cases-

(i) All first five games win ®1

(ii) 4 out of first five and last one win®5C4

(iii) 4 out of first six and last one win®6C4

(iv) 4 out of first seven and last one win ® 7C4

(v) 4 out of first eight and last one win ® 8C4

Total ways of winning the series

= 2 × $\lbrack 1 +^{5}C_{4} +^{5}C_{4} +^{7}C_{4} +^{8}C_{4}\rbrack$

= 2 × 9C5 = $\frac{2.9.8.7.6.5}{5.4.3.2.1}$ = 36 × 7 = 252