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 Three from Nine (Posted on 2006-04-25)
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.

 No Solution Yet Submitted by Vernon Lewis Rating: 3.5000 (4 votes)

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 re(4): Partial Solution | Comment 8 of 12 |
(In reply to re(3): Partial Solution by Jer)

Jer,

Concurr with 9/14.  Out of the 504 permutations, 72 are divisible by 7.

When mixing the numbers there are 108 repeats in the 432 (72*6)  possibilities. This leaves 324 of 504 number combinations that can be rewritten to be divisible by 7. And as you showed 324/504 = 9/14

 Posted by Leming on 2006-04-25 14:19:49

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