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Probable Prime Poser (Posted on 2010-01-19) Difficulty: 2 of 5
A bag contains 10 marbles that are numbered 0 through 9. Precisely three marbles are drawn at random from the bag without replacement.

Determine the probability that a three-digit prime number (with non leading zero) can be constituted by rearrangement of digits corresponding to the three marbles (including the original order of the digits.)

As a bonus determine the corresponding probability if the three marbles were drawn with replacement at the outset.

No Solution Yet Submitted by K Sengupta    
Rating: 1.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
re: bonus solution Comment 4 of 4 |
(In reply to bonus solution by Charlie)

Just simplifying Charlie's bonus solution math.

53 numbers with three distinct digits and 33 with a matching digit can be rearranged to form primes.

But each of the 53 can be formed in 3*2 (ie 6) different ways, if sequence is considered.
And each of the 33 can be formed in three different ways, if sequence is considered.

Considering sequence, 53*6 + 33*3 = 417 distinct numbers can be rearranged to form a prime.  

So the bonus solution is 417/1000. 

  Posted by Steve Herman on 2010-01-19 18:48:22
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