﻿ 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 : Kaysons Education

# 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

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## Question

### Solution

Correct option is

The total number of cases is 6 × 6 × 6 = 63 = 216. The number of favorable ways

= coefficient of xk in (x + x2 +…….+ x6)3

= coefficient of xk – 3 in (1 – x6)3 (1 – x) – 3

= coefficient of xk – 3 in (1 – x) – 3                 [∴ 0 ≤ k – 3 ≤ 5]

= coefficient of xk – 3 in

Thus, the probability of the required event is (k – 1) (k – 2)/432

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