A dice is rolled three times. The probability | vedclass

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(B) The total number of possible outcomes when a dice is rolled three times is $6^3 = 216$.Let the three numbers obtained be $x_1, x_2, x_3$. We requi

Vedclass · Accepted Answer

$\frac{5}{54}$

Vedclass · Answer

(B) The total number of possible outcomes when a dice is rolled three times is $6^3 = 216$.Let the three numbers obtained be $x_1, x_2, x_3$. We require $x_1 This is equivalent to choosing $3$ distinct numbers out of ${1, 2, 3, 4, 5, 6}$,because for any set of $3$ distinct numbers,there is only one way to arrange them in increasing order.The number of ways to choose $3$ distinct numbers from $6$ is given by the combination formula $\binom{6}{3}$.$\binom{6}{3} = \frac{6 	imes 5 	imes 4}{3 	imes 2 	imes 1} = 20$.Thus,the number of favourable outcomes is $20$.The required probability is $\frac{20}{216} = \frac{5}{54}$.

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

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