Three six-faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is k 3 ≤ k ≤ 8 is

Step-by-step solution

The total number of cases is 6 × 6 × 6 = 6 3 = 2 1 6 . The number of favourable ways = coefficient of x k in x + x 2 + ....... + x 6 3 = coefficient of x k - 3 in 1 - x 6 3 1 - x - 3 = coefficient of x k - 3 in 1 - x - 3 [ ∵ 0 ≤ k - 3 ≤ 5 ] = coefficient of x k - 3 in 1 + 3 C 1 x + 4 C 2 x 2 + 5 C 3 x 3 + ...... = k - 3 + 2 C k - 3 = k - 1 C 2 = k - 1 k - 2 2 Thus, the probability of the required event is k - 1 k - 2 432 .