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 bonus solution
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.