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The probability of getting three fives in the first three rolls and non-fives

in the

next three rolls is; P(5,5,5,N5,N5,N5) =

1/6 x 1/6 x 1/6 x 5/6 x 5/6 x 5/6

=

0.002679...

The number of different order in which the fives can come out is given by;

6C3 =

6!/[3!∙(6-3)!] =

20

So the probability that in 6 rolls of a fair die exactly three fives (in any order) will

come out is; P(three

fives any order) =

(20)∙(1/6)3∙(5/6)3 =

0.05358... ~ 5.4%

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Q: What is the probability that 6 rolls of a fair die will show exactly three fives?
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