MHB Dice Probability: 5 Rolls, Increasing Number

[juantheron]

A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is

 

[Evgeny.Makarov]

It's easy to explicitly enumerate all increasing sequences of 5 numbers from {1, ..., 6}.

 

[CaptainBlack]

A Dice is Rolled $5$ times. The Probability of Getting a higher number then the previous number each time is

Because the sequences are increasing all the die rolls are different, as there are only 6 possible outcomes all but one of the outcomes must be present in such a sequence and there is only one order that these can be in, so there are exactly \(6\) increasing sequences of 5 die roll outcomes from a total of \(6^5\) possible sequences of 5 die roll outcomes...

CB