Question 1116827: How many different 5-card poker hands contain exactly two kings?
I tried C(13,5) x C(4,2) x C(11,3) but I kept getting the wrong answer.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! there are 52 cards in the deck.
you draw a hand.
that's 5 cards total.
there are 4 kings in the deck.
there are 48 other cards in the deck.
the number of ways you can get 2 kings is c(4,2) = 6
the number of ways you can get 3 other cards is (c(48,3) = 17296.
the total number of ways you can get 5 cards where 2 are kings and 3 are something else is 6 * 17296 = 103776.
to see how this works, try something a lot simpler.
assume the deck has 4 kings and 1 jack and a queen only.
that's a total of 6 cards.
how many ways can you get a 3 card hand that has 2 kings plus 1 other card.
if we're correct, the number of ways should be c(4,2) * c(2,1) = 12.
let's see if that's true.
let the kings be the letters a,b,c,d.
let the queen be the number 1.
let the jack be the number 2.
you are drawing 3 cards from the deck of 6.
the number of ways you can get 2 kings that are diferent from each other is c(4,2) = 6
that would be:
a,b
a,c
a,d
b,c
b,d
c,d
for each one of these pairs of kings, you can draw either a queen or a jack.
if a queen, you would get:
a,b,1
a,c,1
a,d,1
b,c,1
b,d,1
c,d,1
if a jack, you would get:
a,b,2
a,c,2
a,d,2
b,c,2
b,d,2
c,d,2
that'a total of 12 possible ways.
the method of solution appears to be good with a simple example.
i would try itthe same method with the more complex example and see if it's right.
if not, let me know what the solution is supposed to be and i'll try to see what other method might work.
my solution using this method is c(4,2) * c(48,3) = 103776.
|
|
|
