If a fair die is rolled six times what is the probability th

If a fair die is rolled six times, what is the probability that

(a) each score is obtained exactly once?

(b) a \'6\' is not obtained at all?

Solution

a)

There are 6^6 ways to roll a die six times.

There are 6! ways to get each number once.

Thus,

P = 6! / (6^6) = 0.015432099 [ANSWER]

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b)

There are 5^6 ways to not get a 6 six consecutive times.

Thus,

P = (5^6)/(6^6) = 0.334897977 [answer]