Counting

\({6! \over 2!} = \color{brown}\boxed{360}\)

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We have 6 numbers in the set "2, 2, 5, 6, 8, and 9", so we have 6! to find the different positive 6 digit integers that can be formed.

 

And we have two 2s... which means that we need to divide by 2!

 

That will give us: 6!/2! which is 360 different positive 6 digit numbers