Question

Abhay choses to bat and he scores exactly 50 runs in 12 balls. He makes only zeroes, fours and sixes in these 12 balls. It is also known that he does not score more than 2 zeroes. In how many different ways can he do so?

• A. ¹²C₁₁
• B. 11!x2!
• C. ¹²C₁₀ + ¹²C₁₁.²C₁ + ¹²C₉.³C₂
• D. none of these

Answer 1

The correct option is D

none of these

50 runs can be scored from 12 balls as follows
Option 1:- 11 fours and 1 six = ${}^{12}$C${}_{11}$ .${}^1$C${}_1$
Option 2:- 1 zero + 8 fours + 3 sixes = ${}^{12}$C${}_8$.${}^4$C${}_3$
Option 3:- 2 zeroes+ 5 fours+ 5 sixes = ${}^{12}$C${}_3$.${}^9$C${}_2$

Answer = sum of all 3. option- d