SOLUTION: Please help!! A fair die is rolled 6 times. Find the probability that all 6 rolls are different. Simplify using a fraction in lowest term.

Question 1022636: Please help!!
A fair die is rolled 6 times. Find the probability that all 6 rolls are different. Simplify using a fraction in lowest term.
Found 2 solutions by mathmate, rothauserc:
Answer by mathmate(429) (Show Source): You can put this solution on YOUR website!

Question:Please help!!
A fair die is rolled 6 times. Find the probability that all 6 rolls are different. Simplify using a fraction in lowest term.

Solution:
There are 6^6 permutations when we roll a die 6 times.
There are 6! permutations when we have six distinct digits (1-6).
So probability that all six throws are distinct
=
=
=
= 0.015432 (approximately)
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
The probability of getting any one number is 1/6, then
Given 6 rolls probability of all 6 numbers different is
:
1*(5/6)*(4/6)*(3/6)*(2/6)*(1/6) = 0.0154 = 1.54%
:

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