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)?

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NDA-II 2024 (Maths) Official Paper (Held On: 01 Sept, 2024)
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  1. 5/9
  2. 2/3
  3. 1/3
  4. 1/2

Answer (Detailed Solution Below)

Option 4 : 1/2
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Explanation:

⇒n(S) = 6 × 5 × 4

⇒ n(E) = n (one of the faces shown is an ace.)

=  3(1 × 5 × 4) = 3 × 5 × 4 

⇒ \(P(E) = \frac{3\times 5\times 4}{6\times 5\times4} = \frac{1}{2}\)

∴ Option (d) is correct

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