Problem D

No Power

Five balls are placed in a bag. Each ball is labelled with a \(2\), \(4\), \(6\), \(8\), or \(10\), with no ball having the same label as any other. Adeleke randomly chooses a ball, records the integer on the ball, and replaces the ball into the bag. Then Bo randomly chooses a ball, records the integer on the ball, and replaces the ball into the bag. Finally, Carlos randomly chooses a ball, records the integer on the ball, and replaces the ball into the bag.

Determine the probability that the product of the three recorded integers is not a power of \(2\).