BattleDroids describes regiments as containing 108 BattleMechs (in 3 battalions of 36), and the regimental commander as Duke of a whole planet. MechWarrior 1st Edition counts about 450 settled worlds in the five Successor States.
108 regiments * 450 commanders = 48,600 'Mechs
BattleForce 1st Edition says the Houses reorganized to 128 'Mechs per regiment (in 3 battalions of 40 plus an 8 'Mech regimental command group). If I recall correctly, it also says this new organization was copied from Wolf's Dragoons.
48,600 / 128 = 379 2/3 regiments
Wolf's Dragoons add 5 regiments plus Zeta Battalion to that total.
379 2/3 regiments + 5 1/3 regiments = 385 regiments
