What is the probability that a player is dealt 3 kings in a single euchre hand?
This is a hypergeometric distribution problem.  Luckily, calculators exist that let you just plug in the numbers and get an answer.  I used this one with

Population size = 24 (the size of the deck)

Number of successes in population = 4 (the total number of kings)

Sample size = 5 (the number of cards in your hand)

Number of successes in sample = 3 (the number of kings you are interested in)

The results show that the chances of getting exactly 3 kings is 1.79%.  If you also include hands with 4 kings, it goes up to 1.84%.