Question

Find the probability of being dealt three kings in five-card poker from a standard deck of fifty-two playing cards.

Answer 1

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:

`(52!)/(5!(52-5)!)=(52!)/(5!47!)=2598960`

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:

`4\cdot((52-4)!)/(2!(52-4-2)!)=4\cdot(48!)/(2!46!)=4512`

Therefore, the probability of being dealt three kings in five-card poker from a standard deck is given by:

`(4512)/(2598960)=(282)/(162435)=(94)/(54145)`