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.

(In reply to computer solution to part 1 by Charlie)

BTW, in decimal approximation, the non-replacement version probability amounts to .4416666666666667, and the replacement version, of course, to .417.

Posted by Charlie on 2010-01-19 17:04:08