If a die is rolled three times,then the proba | vedclass

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(B) The total number of possible outcomes when a die is rolled three times is $6^3 = 216$.We need to select three distinct numbers from the set $\{1,

Vedclass · Accepted Answer

$\frac{5}{54}$

Vedclass · Answer

(B) The total number of possible outcomes when a die is rolled three times is $6^3 = 216$.We need to select three distinct numbers from the set $\{1, 2, 3, 4, 5, 6\}$ such that they appear in strictly increasing order.Any selection of $3$ distinct numbers from $6$ can be arranged in exactly one way in strictly increasing order.The number of ways to choose $3$ distinct numbers from $6$ is given by $^6C_3 = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Thus,the number of favorable outcomes is $20$.The required probability is $\frac{20}{216} = \frac{5}{54}$.

If a die is rolled three times,then the probability of getting a larger number on its face than the previous number each time is:

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