Question

A die is rolled three times. The probability of getting a number larger than the previous number each time is

• A. $11/72$
• B. $5/54$
• C. $19/216$
• D. $7/18$

Answer 1

The correct option is B $5/54$

Total number of ways $=6\times 6\times 6$
$\therefore n\left(S\right)=216$

The number of favorable ways $={}^6{C}_3$
$\therefore n\left(E\right)={}^6{C}_3$

Hence, required probability $=\frac{{}^6{C}_3}{6\times 6\times 6}=\frac{5}{54}$