JEE MAIN - Mathematics (2023 - 6th April Evening Shift - No. 11)
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 :
3
4
1
2
Explanation
Total number of outcomes $=6 \times 6 \times 6=216$
Number of outcomes getting different numbers on the three dice are ${ }^6 P_3=\frac{6 !}{3 !}=120$
$\therefore$ Required probability $=\frac{120}{216}=\frac{5}{9}$
$\therefore p=5$ and $q=9$
$\therefore q-p=9-5=4$
Number of outcomes getting different numbers on the three dice are ${ }^6 P_3=\frac{6 !}{3 !}=120$
$\therefore$ Required probability $=\frac{120}{216}=\frac{5}{9}$
$\therefore p=5$ and $q=9$
$\therefore q-p=9-5=4$
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