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  • Three dice are rolled. If the probability of getting different numbers on the three dice is <img alt="\mathrm{\frac{p}{q}}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%

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

Option: 1

1


Option: 2

2


Option: 3

4


Option: 4

3


Answers (1)

best_answer

\begin{aligned} & \text { Fav. }=\frac{\left({ }^6 \mathrm{C}_3\right)(3 !)}{6 \times 6 \times 6} \\ & =\frac{(20)(6)}{6 \cdot 6 \cdot 6}=\frac{20}{36}=\frac{5}{9}=\frac{\mathrm{p}}{\mathrm{q}} \\ & \left.\begin{array}{l} \mathrm{p}=5 \\ \mathrm{q}=9 \end{array}\right] \Rightarrow \mathrm{q}-\mathrm{p}=4 \\ & \end{aligned}

Correct Answer is option 3

Posted by

Ritika Harsh

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