# dice probability

#### jacks

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

#### Evgeny.Makarov

##### Well-known member
MHB Math Scholar
It's easy to explicitly enumerate all increasing sequences of 5 numbers from {1, ..., 6}.

#### CaptainBlack

##### Well-known member
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