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## Prime Nine

Probability puzzles require you to weigh all the possibilities and pick the most likely outcome.

 Puzzle ID: #40004 Fun: (2.56) Difficulty: (2.01) Category: Probability Submitted By: RampaginRobo

There are 9! ways to arrange the digits 1-9 to form a 9-digit number.

E.g. 345, 987, 126

If you know this, then if I wrote all 9! possibilities on cards (1 way per card), and I asked you to select one at random; what is the probability that the number you selected is prime?

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 Scubee Jan 11, 2008 9 ways to arrange the digits 1-9 to form a 9-digit number? I'm confused. If my calculations are correct, wouldn't there be 362880 (9*8*7*6*5*4*3*2*1) possible ways to arrange 1-9 into a nine digit number? This doesn't change the answer but confusing still. RampaginRobo Jan 11, 2008 Scubee, 9! means 9 factorial which is 362, 880. Holo Jan 12, 2008 Actually, there would be 3,486,784,401 ways calmsavior Jan 13, 2008 Congratulations on having the first approved teaser with a 4 in the ten-thousands position. RampaginRobo Jan 20, 2008 Firstly, thanks calmsavior! And secondly, where did your idea come from Holo? bookwrmKP Feb 01, 2008 Wow. I would have never figured that out.... I guess I'm not as smart as you guys... Very clever! jsdodgers Apr 03, 2008 One problem. 9! means 9*8*7*6*5*4*3*2*1, not 9+8+7+6+5+4+3+2+1. jsdodgers Apr 03, 2008 Nevermind my last comment. I understand where you got the 9+8+7+6+5+4+3+2+1 from now. scott8anthony Apr 11, 2008 I must say this one incorporates a simple rule and disguises it very well; good job! stephiesd May 03, 2008 Whoo. This teaser was amazing. It actually took me a minute... But then I got it. (With the hint... ) Lord_Hawk Jan 04, 2009 I like the way this simple problem disguises such a simple division rule. It took me a while to notice it. I must boast that I didn't have to look at the hint though opqpop Sep 27, 2010 Too easy. Which numbers are prime? Oh look, 1+...+9 = 45 which is divisible by 3 and you're done. daquity36 Jun 25, 2012 This problem seems incorrect.. What about #'s such as 127, 137, 149, 157 ... etc? http://en.wikipedia.org/wiki/List_of_prime_numbers daquity36 Jun 25, 2012 Oops never mind. I thought this problem was for 3 digits.