Question

Three fair dice are rolled, one red, one green and one blue. What is the probability that the upturned faces of the three dice are all of different numbers?

Answer 1

Answer:   $\dfrac{5}{9}$

Step-by-step explanation:

When we throw a die , Total outcomes =6

When we throw 3 dice , Total outcomes = 6 x 6 x 6 = 216 [by fundamental counting principle]

Given : Three fair dice are rolled, one red, one green and one blue.

Favorable outcomes : When the upturned faces of the three dice are all of different numbers i.e. no repetition of numbers allowed

By Permutations , the number of favorable outcomes = $^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120$

The probability that the upturned faces of the three dice are all of different numbers = $\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}$

$=\dfrac{120}{216}=\dfrac{5}{9}$

The probability that the upturned faces of the three dice are all of different numbers  is $\dfrac{5}{9}$ .