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14.Probability
medium
If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $i^{\text {th }}$ roll than the number obtained in the $(i-1)^{\text {th }}$ roll, $i=2,3$, is equal to :
A
$3 / 54$
B
$2 / 54$
C
$5 / 54$
D
$1 / 54$
(JEE MAIN-2024)
Solution
Favourable cases $={ }^6 \mathrm{C}_3$
Total out comes $=6^3$
Probability of getting greater number than previous
$\text { one }=\frac{{ }^6 \mathrm{C}_3}{\mathrm{r}^3}=\frac{20}{216}=\frac{5}{54}$
Standard 11
Mathematics
