Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is `k(9 le k le 14)`, is

Question

Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is k(9≤k≤14), is A. 21k-k2-83 216 B. k2-3k+2 432 C. 21k-k2-83 432 D. none of these Select the correct answer from above options

Answer 1

Correct Answer - A Proceeding as in Example 14, we have Favourable number of elementary events = Coeff.of xk-3 in (1-x6)3(1-x)-3 Coeff.of xk-3 in (1-.3C1x6+..)(1-x)-3[∵9≤k≤14∴6≤k-3≤11] =Coeff.of xk-3 in (1-x)-3-.3C1{Coeff.of xk-9 in (1-x)-3} =.k-3+3-1C3-1-.3C1×.k-9+3-1C3-1 .k-1C2-3×.k-7C2 = (k-1)(k-2) 2 - 3(k-7)(k-8) 2 =21k-k2-83 Hence, probability of required event = 21k-k2-83 63