Question
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

None of these



medium
Solution
The total number of cases is 6 × 6 × 6 = 6^{3} = 216. The number of favorable 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
Thus, the probability of the required event is (k – 1) (k – 2)/432
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