How do you calculate the number of management options issued, for a take-private?

How do you calculate the number of management options issued, for a take-private, if you're just given information like "Assume management receives options ($X exercise price) that represent 10% of the fully diluted company, post transaction"

I know you need to do TSM as part of the calculation for Total Shares Outstanding. However, how do you get to the NUMBER of management options issued, in the first place? 

For private companies it seems easy, just:

Ending equity value

Plus: management option proceeds: Initial equity value/(1- % management options)  * management options     ... to factor dilution 

Less: management options: Ending equity value *  % management options

= Value to PE firm
But what about public companies?