There is a total of four kings in a standard deck.
There total number of 5-card combinations that is possible to draw in a 52 cards deck is given by:
[tex]\frac{52!}{5!(52-5)!}=\frac{52!}{5!47!}=2598960[/tex]The total number of ways by which we can combine three kings between four is 4!/3! = 4. Then, the total number of 5 cards combinations that includes exactly 3 kings is given by:
[tex]4\cdot\frac{(52-4)!}{2!(52-4-2)!}=4\cdot\frac{48!}{2!46!}=4512[/tex]Therefore, the probability of being dealt three kings in five-card poker from a standard deck is given by:
[tex]\frac{4512}{2598960}=\frac{282}{162435}=\frac{94}{54145}[/tex]