What is the probability that three unbiased dices to roll such that abc. Extrapolate to five random number generators (1 to n)

Question

What is the probability that three unbiased dices to roll such that a>b>c. Extrapolate to five random number generators (1 to n)

Accepted Answer

Probability of rolling three unbiased dices such that a>b>c and extrapolating to five random number generators.

The probability of rolling three unbiased dices such that a>b>c is 1/216.
To extrapolate to five random number generators, we need to calculate the probability of generating five random numbers such that the first is greater than the second, the second is greater than the third, and so on.
The probability of generating five random numbers such that the first is greater than the second, the second is greater than the third, and so on is (n choose 5) / 120.
Where n is the range of the random number generators.
For example, if n=10, the probability of generating five random numbers such that the first is greater than the second, the second is greater than the third, and so on is (10 choose 5) / 120 = 0.252.

What is the probability that three unbiased dices to roll such that a>b>c. Extrapolate to five random number generators (1 to n)