Question

In a shooting competition a man can score 5, 4, 3, 2, 1 or 0 points for each shot. Then the number of different ways in which he can score 10 in seven shots is-

• A. 6538
• B. 6539
• C. 6537
• D. None of these

Answer 1

Answer: (A)

6538

Answer 2

The number of ways of making 30 in 7 shots is the coefficient of x³⁰ in

(x⁰ + x² + x³ + x⁴ + x⁵)⁷

̃ (x⁰ + x² + x³ + x⁴ + x⁵)⁷ = [x⁴ (x +1) + (x³ + x² + 1)]⁷

̃ x²⁸ (x + 1)⁷ + 7C₁ x²⁴ (x+1)⁶ (x³ + x² +1) + 7C₂ x²⁰(x +1)⁵ (x³ + x² + 1)² +….

So, coefficient of x³⁰ is 7C₅ + 7C₁ (⁶C₃ + ⁶C₂ + 1) +7C₂

( ⁵C₁ + 2)

= 21 + 7 (20 + 15 + 1) + 21 (5 + 2) = 420