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

Step-by-step solution

Required number of ways = Coefficient of x 10 in x 0 + x 1 + . . . + x 5 7 = coefficient of x 10 in 1 - x 6 7 1 - x - 7 = coefficient of x 10 in 1 - 7 x 6 1 - x - 7 (Neglecting the terms higher than x 10 ) = coefficient of x 10 in 1 - x - 7 - 7 x 6 1 - x - 7 = 16 C 6 - 7 . 10 C 4 = 6538