Three perfect dice are rolled. Under the condition that no two show...

Three perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?

Options

A $\frac{5}{9}$
B $\frac{2}{3}$
C $\frac{1}{3}$
D $\frac{1}{2}$

Correct answer

D. $\frac{1}{2}$

Step-by-step solution

When three dice rolled and

no two show same faces

\begin{aligned} & \mathrm{n}(\mathrm{ s})=6 \times 5 \times 4 \\ & \mathrm{n}(\mathrm{E})=\mathrm{n}(\text{ one of the faces shown is an one })=3(1 \times 5 \times 4) \\ & =3 \times 5 \times 4 \\ & \mathrm{P}(\mathrm{E})=\frac{3 \times 5 \times 4}{6 \times 5 \times 4}=\frac{1}{2} \end{aligned}

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