Three positive integers are chosen at random without replacement from 1,2,....,64.
What is the probability that the numbers chosen are in geometric sequence?

Order of choice doesn't matter. For example, 4-1-2 would qualify as
numbers in geometric sequence.

__Bonus Question__:

Generalise this result (in terms of n) covering the situation where three positive integers are chosen at random without replacement from 1,2,.....,n^{2}.

**
p=54/41664=0.001296 ....***edited*

i have counted 54 possible triplets from (1 2 4 ) to (49 56 64 )

REMARK:

COMPARING MY MANUALLY PRODUCED LIST WItH

THAT OF CHARLIE'S - I fouund that I missed four triplets

, so the correct answer is

**58/41664 = approx. 0.001392 **

*Edited on ***February 28, 2013, 3:36 pm**