Question

In a shooting competition a man can score 5, 4, 3, 2 or 0 points for each shot. Then the number of different ways in which he can score 30 in seven shots is –

• A. 419
• B. 418
• C. 420
• D. 421

Answer 1

Answer: (C)

420

Answer 2

Number of ways of making 30 in 7 shots is,

Coefficient of x³⁰ in (x⁰ + x² + x³ + x⁴ + x⁵)⁷

Ž Coefficient of x³⁰ in {(x⁰ + x² + x³) + x⁴ (x + 1)}⁷

Ž Coefficient of x³⁰ in {x²⁸(x + 1)⁷ + ⁷C₁x²⁴

(x + 1)⁶.(1 + x² + x³)+ ⁷C₂ x²⁰ (x + 1)⁵ (x³ + x + 1)² +….}

Ž ⁷C₅ + ⁷C₁ (⁶C₃ + ⁶C₂ + ⁶C₀) + ⁷C₂ (⁵C₁ + 2)

Ž 21 + 252 + 147 = 420

Hence (3) is correct answer.