What the number of combinations of a set on numbers?

In the United States Air Force, all airmen have the option to wear combination caps, but only Field-Grade and General Officers, (Major and above), are required to own one. The cap of enlisted members has the insignia within a metal circle, while the Company-Grade (2dLt-1stLt-Captain) Officer version has a larger insignia without the metal circle. Field Grade Officers have clouds and lightning bolts on the bill. General Officer caps add an extra set of clouds and bolts, while the cap of the Chief of Staff of the United States Air Force adds clouds and bolts around the entire band. The clouds and bolts are jokingly referred to as "farts and darts."