Duplication not allowed!
Probability
Level
2
A fair 6-sided die has the numbers 1, 2, 3, 4, 5, 6 on its faces.
If you roll it 5 times, what are the chances that no number comes up more than once?
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1 solution
Moderator note:
Simple standard approach.
The first roll comes up with a number.
There is a 5/6 chance the second roll comes up with a different one.
If that happens, 2 numbers are eliminated, so there is a 4/6 chance the third roll doesn't provide a duplicate.
Similarly, your duplicate-avoiding chance on the 4th roll is 3/6 and on the 5th roll 2/6.
So the total chance is 5/6 * 4/6 * 3/6 * 2/6 = 5/6 * 2/3 * 1/2 * 1/3 = 10/108 = 5/54