Answer: [tex]\dfrac{5}{9}[/tex]
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 = [tex]^6P_3=\dfrac{6!}{(6-3)!}=\dfrac{6!}{3!}=6\times5\times4=120[/tex]
The probability that the upturned faces of the three dice are all of different numbers = [tex]\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
[tex]=\dfrac{120}{216}=\dfrac{5}{9}[/tex]
The probability that the upturned faces of the three dice are all of different numbers is [tex]\dfrac{5}{9}[/tex] .
