A dice is rolled 3 times, what is the probabilty of getting a no. greater than last no. each time?

The maximum number that we can get is 6 in the third roll.

Then, the second can have 5, 4, 3, 2.

and for each of these the first roll can have (4,3,2,1), (3,2,1), (2,1), (1).

Hence there are 4+3+2+1 = 10 ways.

Similarly if the third roll gives a number 5 then,

there are 6 ways.

Similarly if the third roll gives a number 4 then,

there are 3 ways.

Similary if the third roll gives a number 3 then there is only one way.

Hence the probability = 20/216 = 5/54.

Regards,

Team,

TopperLearning.