+4 You are playing a poker game called "Omaha" and are dealt 4 cards from a standard 52 card deck. How many possible combinations of hands can you be dealt that contain both at least one Ace and at least one King? Please explain your answer.
+118687 Hi Lance and Fellowes,
You are playing a poker game called "Omaha" and are dealt 4 cards from a standard 52 card deck. How many possible combinations of hands can you be dealt that contain both at least one Ace and at least one King? Please explain your answer.
It would be easier for me to check if you had given some number answers
I am not sure if my logic is the same as yours or not.
A for ace, K for king, x for any other card
1ace
AKxx 4*4* 44C2 = 15136
AKKx 4*4C2*44 = 1056
AKKK 4* 4C3 = 16
2 aces
AAKx 4C2 * 4 * 44 = 1056
AAKK 4C2 * 4C2 = 36
3 aces
AAAK 4C3 * 4 = 16
15136+1056+16+1056+36+16 = 17316
That is what I think anyway :)
+1316 To do this you have to add a lot of combinations
To have at least mean you can have more so you have to add up all the combinations where you have exact amounts.
Start with only aces and kings
There are 4 aces and 4 kings to select from.
There are
4C3 + 4C1 to draw 3 aces and 1 king.
4C2 + 4C2 to draw 2 aces and 2 kings
4C1 + 4C3 to draw 1 aces and 3 kings
Then do this with the other 46 cards
4C2 + 4C1 + 46C1 to draw 2 aces and 1 king and 1 of something else.
4C1 + 4C2 + 46C1 to draw 1 ace and 2 kings and 1 of something else.
4C1 + 4C1 + 46C2 to draw 1 ace and 1 king and 2 of something else.
Add all these up to get the total number of ways you can draw 4 cards with at least 1 ace and 1 king.
On the site calc use this nCr(4, 3) for 4C3
One of moderators should check that I not make a mistake. Maybe there is a easier way to do this too.
+118687 Hi Lance and Fellowes,
You are playing a poker game called "Omaha" and are dealt 4 cards from a standard 52 card deck. How many possible combinations of hands can you be dealt that contain both at least one Ace and at least one King? Please explain your answer.
It would be easier for me to check if you had given some number answers
I am not sure if my logic is the same as yours or not.
A for ace, K for king, x for any other card
1ace
AKxx 4*4* 44C2 = 15136
AKKx 4*4C2*44 = 1056
AKKK 4* 4C3 = 16
2 aces
AAKx 4C2 * 4 * 44 = 1056
AAKK 4C2 * 4C2 = 36
3 aces
AAAK 4C3 * 4 = 16
15136+1056+16+1056+36+16 = 17316
That is what I think anyway :)
+1316 OK I make 2 mistakes
I put 46 instead of 44 for the leftover cards (I left the jokers in hahaha)
I add instead of multiplying the combinations going across.
After fixing these mistakes I get this which is the same as your answer :)
NCR(4,3) * NCR(4,1) = 16
NCR(4,2) * NCR(4,2) = 36
NCR(4,1) * NCR(4,3) = 16
NCR(4,2) * NCR(4,1) * NCR(44,1) = 1056
NCR(4,1) * NCR(4,2) * NCR(44,1) = 1056
NCR(4,1) * NCR(4,1) * NCR(44,2) = 15136
16+36+16+1056+1056+15136 = 17316
Thank you Miss Melody.
