Three dice are rolled. If probability of getting different numbers on three dice is frac{p}{q} , whe

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14.Probability

hard

Three dice are rolled. If the probability of getting different numbers on the three dice is $\frac{p}{q}$, where $p$ and $q$ are co-prime, then $q- p$ is equal to

A

$4$

B

$3$

C

$1$

D

$2$

(JEE MAIN-2023)

Solution

Total number of ways $=6^3=216$

Favourable outcomes ${ }^6 p _3=120$

$\Rightarrow \text { Probability }=\frac{120}{216}=\frac{5}{9}$

$\Rightarrow p =5, q =9$

$\Rightarrow q – p =4$

Standard 11

Mathematics

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