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A dice is rolled three times, find the p...

A dice is rolled three times, find the probability of getting a larger number than the previous number each time.

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Total number of cases = `6^(3) = 216`.
If a larger number appears than the previous number each time, all the three number are distinct.
Three numbers can be selected from six numbers in `.^(6)C_(3) = 20` ways and there is only one way in which three selected numbers can appear.
Hence, required probability = `(20)/(216) = (5)/(54)`
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