Question

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

• A. $\frac{5}{216}$
• B. $\frac{5}{54}$
• C. $\frac{1}{6}$
• D. $\frac{5}{36}$

Answer 1

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

Total outcomes $=6^3=216$

Three numbers can be arranged in ascending order.

Favourable outcomes $={}^6{C}_3\times 1$

Probability $\frac{{}^6{C}_3}{216}=\frac{20}{216}=\frac{5}{54}$