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

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

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

[spoiler]OA=D[/spoiler]

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Vincen wrote:
Wed Jun 24, 2020 2:07 am
What is the probability of rolling three six-sided dice, and getting a different number on each die?

A. 1/12
B. 1/3
C. 4/9
D. 5/9
E. 7/18

[spoiler]OA=D[/spoiler]

Solution:

Since the number of the first die can be any number on the die, its probability is 6/6. However, the number on the second die has to be different from that of the first, so its probability is 5/6. Lastly, the number on the third die has to be different from those of the first two, so its probability is 4/6. Therefore, the probability of rolling three six-sided dice and getting a different number on each die is:

6/6 x 5/6 x 4/6 = 1 x 5/6 x 2/3 = 10/18 = 5/9

Answer: D

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