Barb have 33.180.840.000.000 possible combinations of hes skills.
but i'm sure 33.000.000.000.000 of these are not viable at all
skills cant be selected twice or more.
runes are counted in as a possibility for each skill.
times passives and every combo there is without using same twice
i dare you to find any errors.
--edit--
added note about not using unruned skills
Example:
BARB: 22 skills 5 runes each + 16 passives in 3 diffrent slots
you cant have same skill whit different rune
NOT counting unruned skills
(22*5)*(21*5)*(20*5)*(19*5)*(18*5)
(skill*runes)*(remaining skills*runes)*(remaining skills*runes)*(remaining skills*runes)*(remaining skills*runes)
(22*5)*(21*5)*(20*5)*(19*5)*(18*5) = 9.875.250.000
9.875.250.000*16=158.004.000.000 (passives)
158.004.000.000*15=2.370.060.000.000 (remaining passives)
2.370.060.000.000*14=33.180.840.000.000 (remaining passives)
Barb have 33.180.840.000.000 possible combinations of hes skills.
but i'm sure 33.000.000.000.000 of these are not viable at all
skills cant be selected twice or more.
runes are counted in as a possibility for each skill.
times passives and every combo there is without using same twice
i dare you to find any errors.
--edit--
added note about not using unruned skills