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: Partial Solution - ? with no answer of my own by Leming)

If the first two numbers total to 9 (like 3 and 6), you can always make the third digit 9 to preserve the divisibility by 9.  However, you are correct to have concerns, I was incorrect as you and Jer have shown.

I just did a "brute force" on the numbers in an excel spreadsheet and did find that the probability that the number will be divisible by 7 is 1/7.  Although I'm still perplexed as to how to explain why...

Posted by tomarken on 2006-04-25 13:31:25