Question

Abhay chooses to bat and he scores exactly 50 runs in 12 balls. He makes only zeroes, fours and sixes in these 12 balls. 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

Option (d)

50 runs can be scored from 12 balls as follows

Case 1: 11 fours and 1 six = ${}^{12}{C}_{11}{.}^1{C}_1$

Case 2: 1 zero + 8 fours + 3 sixes = ${}^{12}{C}_8{.}^4{C}_3$

Case 3: 2 zeroes+ 5 fours+ 5 sixes = ${}^{12}{C}_5{.}^7{C}_5$

Case 4: 3 zeroes + 7 sixes + 2 fours = ${}^{12}{C}_3{.}^9{C}_2{.}^7{C}_7$

Answer = sum of all 4. option- d