Question

In an exciting finish to a T - 20 cricket match between MI and RCB, the MIs require 10 runs in the last 3 balls to win. If any one of the scores 0, 1, 2, 3, 4, 6 can be made from a ball and no wides or no-balls are bowled then in how many different sequences can batsmen make exactly 10?

• A. 36
• B. 21
• C. 35
• D. 22

Answer 1

The correct option is B

21

A + B + C = 10, Where 0 ≤ A, B, C ≤ 6
Number of solution of given equation is (${}^{13}{C}_2-3{\times }^5{C}_2$). But A, B and C are not equal to 5. Number of cases which are not possible (5, 5, 0), (1, 4, 5) and (2, 3, 5). Total number of cases which are not possible = 3 + 6 + 6= 15.

Total number of different sequences = ${}^{13}{C}_2-3{\times }^5{C}_2$- 15 = 21