A die is rolled thrice, find the probability of getting a larger number each time than the previous number.

Options

A. `(5)/(216)`
B. `(5)/(54)`
C. `(1)/(6)`
D. `(5)/(36)`

Answer

B

Explanation

Total number of cases `=6xx6xx6=216`
Let the second number be I (clearly, ` lt i lt 6`), then the first number can be chosen in (i-1) ways and the third number can be chosen in (6-i) ways
Hence, the number of ways is (i-1)(6-1).
Therefore, i can take values 2 to 5.
Favourable number of cases `underset(i=2)overset(5)Sigma(i-1)(6-i)`
`=1xx4+2xx3+3xx2+4xx1=20`
Hence, required probability`=(20)/(216)=(5)/(54)`