Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is `k(3 le k le 8)`, is

Question

Three six-faced dice are thrown together. The probability that the sum of the numbers appearing on the dice is k(3≤k≤8), is A. k2 432 B. k(k-1) 432 C. (k-1)(k-2) 432 D. k(k-1)(k-2) 432 Select the correct answer from above options

Answer 1

Correct Answer - C The total number of elementary events associated to the random experiment of throwing three dice is 6×6×6=63. Favourable number of elementary events =Coeff. Of xk in (x+x2+x3+..+x6)3 =Coeff. Of xk-3 in ( 1-x6 1-x )3 = Coeff. of xk-3 in (1-x6)3(1-x-3 = Coeff. of xk-3 in (1-x)-3 [∵0≤k-3≤5] =.k-3+3-1C3-1[∵ Coeff.ofxn in (1-x)-r=.n+r-1Cr-1] =.k-1C2= (k-1)(k-2) 2 . ∴ Requried probability = (k-1)(k-2) 2×63 = (k-1)(k-2) 432