What is the theoretical probability of being dealt exactly one ace in a 5-card hand from a standard 52-card deck?

Using the combination formula, there are 4 C 1 = 4 ways to get exactly 1 ace
There are 48 C 4 = 194,580 ways to get 4 other cards (that aren't aces)

So there are 4*194,580 = 778,320 different ways to get a five card hand with 1 ace plus 4 other non-ace cards

There are 52 C 5 = 2,598,960 ways to draw 5 cards

Divide the values to get: (778,320)/(2,598,960) = 0.29947363560809

So that's roughly 0.2995 which is equivalent to 29.95%