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Picking numbers (Posted on 2015-07-17) Difficulty: 3 of 5
Bernardo randomly picks 3 distinct numbers from the set (1; 2; 3; 4; 5; 6; 7; 8; 9) and arranges them in descending order to form a 3-digit number.
Silvia randomly picks 3 distinct numbers from the set (1; 2; 3; 4; 5; 6; 7; 8) and also arranges them in descending order to form a 3-digit number.

What is the probability that Bernardo's number is larger than Silvia's number?
Source: AMO

See The Solution Submitted by Ady TZIDON    
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re(2): Analytical Solution (spoiler) | Comment 4 of 7 |
(In reply to re: Analytical Solution (spoiler) by Charlie)

Yes, you are correct, Charlie, and I am not.

If they disregard ties, the probability is 111/166.

In order for the probability to be exactly 2/3, the digit 9 would need to be excluded in the event of a tie.

  Posted by Steve Herman on 2015-07-18 21:34:15
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