Nine marbles numbered 1 to 9 are placed in a barrel and three are drawn out, without replacement. Determine -:

1. The probability that the three digit number formed from the marbles in the order drawn is divisible by (a) Five (b) Seven (c) Nine.
2. The probability that a three digit number can be formed by rearranging the marbles drawn, that is divisible by (a) Five (b) Seven (c) Nine.

(In reply to re(2): Partial Solution - ? with no answer of my own by tomarken)

I just got done brute forcing it myself.  72 out of 504 combos are divisible by 7 which is 1/7.

For part b, though some combos work in more than one way (789 forms two numbers that work for example - 798 and 987) and more than expected don't work at all.  Of the 84 combinations, only 54 have a working permutation.  54/84 = 9/14 which is quite a bit less than 6/7

Posted by Jer on 2006-04-25 13:40:54