Question

What is the probability of rolling three six-sided dice, and getting a different number on each die?

Answer 1

For the first die, we can roll any one of six numbers. For the second die, we can roll any number save for the number we rolled on the first die, giving us 5 possibilities. For the third die, we can roll four different numbers (we can’t roll the number we rolled on the first or second die.

6 x 5 x 4 = 120 possibilities out of 216 total possibilities. (For total possibilities we get 6 x 6 x 6 = 216).

120/216 = 5/9

Answer 2

Answer:

Three six sided dice so Sample space n(s)=6^3

Event E=Getting Different number on each die.

n(E)=6C3*3! ;

that is we can select the 3 different numbers in 6C3 ways and we can arrange these 3 different numbers in 3! ways.

p(E)=n(E)/n(S)

=6C3*3!/6^3

=5/9;

p(E)=5/9.