91Ó°ÊÓ

Three 6-sided, a blue, a yellow, a red dices are given.

The value on the blue dice is less than the value on the yellow dice is less than the value on the red dice.

$\text{Number of ways of selecting}r\text{distinct objects out of}p\text{distinct objects is}\left(\begin{array}{l}p\\ r\end{array}\right)$

$\text{Number of ways of arranging}r\text{distinct objects is}r\text{!}$

$\text{Probability of an event with discrete outcomes}=\frac{\text{Number of favorable outcomes}}{\text{Number of total outcomes}}$

Sample space is all the possible combinations of values on three dice $6^3=216$

For no two values to be equal, selecting the value on the first dice in $\frac{6}{1}$ways, then selecting the value for the second dice in $\frac{5}{1}$ways and selecting value for the third dice in $\frac{4}{1}$ways.

Hence, total number of possible outcomes so that no two values of dice are equal $6×5×4$

Probability that no two dice are equal$=\frac{6×5×4}{6^3}=\frac{5}{9}=0.55$

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