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 Probable Prime Poser (Posted on 2010-01-19)
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)

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 computer solution to part 1 | Comment 1 of 4

There are 53 unique sets of 3 different digits that can form 3-digit primes

`digits    primes`
`013       103014       401016       601017       107 701019       109035       503037       307049       409059       509067       607079       709 907089       809124       241 421125       251 521127       127 271128       281 821134       431136       163 613 631137       137 173 317139       139 193145       541146       461 641149       149 419 491 941157       157 571 751167       167 617 761169       619 691179       179 197 719 971235       523236       263238       283 823239       239 293257       257269       269278       827289       829346       463 643347       347 743349       349 439356       563 653358       853359       359 593 953367       367 673368       683 863379       379 397 739 937389       389 839 983457       457 547467       467 647478       487479       479 947569       569 659578       587 857589       859679       769 967`

so that's 53 digit sets out of the C(10,3) = 120 equally likely possible sets of 3 digits chosen.

The probability is 53/120.

 Posted by Charlie on 2010-01-19 13:08:32
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