Question

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

• A. $\frac{5}{27}$
• B. $\frac{5}{54}$
• C. $\frac{5}{81}$
• D. $\frac{5}{63}$

Answer 1

The correct option is B $\frac{5}{54}$

Exhaustive number of cases is $6^3=216$
Now, if a larger number appears than the previous number each time, all the three numbers are distinct.
Three numbers can be selected from six numbers in ${}^6{C}_3$ ways and there is only one way in which three selected numbers can appear.
Hence,
Required probability $=\frac{20}{216}=\frac{5}{54}$