Battery life calculation parallel vs series
Think of it this way, you get what you pay for, and you're paying for Joules, watt.hours, energy. This is, if you like, the financial restatement of Conservation of Energy. When in doubt in physics, follow the energy!

A 3.2v 3Ah cell holds 9.6Wh. If you have 10 of them, you will have a total of 96 Wh available. It doesn't matter how you rearrange the cells, you will still have the same total energy available.

If they are in series, then 96Wh at 32v is 3Ah, the same as a single cell. As the current has to pass through each in turn, that makes sense. 

If they are in parallel, then 96Wh at 3.2v is 30Ah. As their currents all add up in parallel, this too makes sense.

It still holds if you make a (say) 2s5p array of 6.4v, which will show 15Ah for the same 96Wh energy.