- #1
mr_coffee
- 1,629
- 1
Hello everyone,
Another example from the book I'm going over and I'm not exactly sure how they got their answer:
The game of poker is played with an ordinary deck of cards. Various five-card holdings are given special names.
a. how many 5 card poker hands contain two pair?
Well I'm looking at the list, and I see two pair defined as this:
Two cards of one denomination, two cards of a second denomination, and a 5th card of a thrid denomination.
They said:
consider forming a hand with two paris as a four-step process:
Step 1: Choose the two denominations for the pairs.
Step 2: Choose 2 cards from the small denomination
Step 3: choose 2 card from the larger denomination
Step 4: choose one card from the remianing.
When they say denomination do they mean like:
A,2,3,4,5,6,7,8,9,10,J,Q,K
also why do they say choose 2 cards rfom the small and large denomination? couldn't u do it by getting like 2 kings, and 2 10's, and 1 other card like a 2?
These are all large denominations.
When i did this problem i thought it would be solved like this:
You have 52 cards to pick from, but you only want 2 denominations, so
Step 1: 52 choose 2
Step 2: You already used 2 cards so you only have 50 to choose from now, so 50 choose 2
Okay now you should have 4 cards, now you only need 1 more card, but you can't choose a card you picked in step 1 or 2, so u must take 52-4 = 48, 48 choose 2
(52 choose 2) * (50 choose 2) * (48 choose 1)
But they did it the following way:
total number of hands with two pairs:
Step 1: 13 choose 2
Step 2: 4 choose 2
step 3: 4 choose 2
step 4: 44 choose 1
i'm not sure how they got this...
Also the 44 choose 1, I am not sure how they got 44. Any explanation would be great!
Another example from the book I'm going over and I'm not exactly sure how they got their answer:
The game of poker is played with an ordinary deck of cards. Various five-card holdings are given special names.
a. how many 5 card poker hands contain two pair?
Well I'm looking at the list, and I see two pair defined as this:
Two cards of one denomination, two cards of a second denomination, and a 5th card of a thrid denomination.
They said:
consider forming a hand with two paris as a four-step process:
Step 1: Choose the two denominations for the pairs.
Step 2: Choose 2 cards from the small denomination
Step 3: choose 2 card from the larger denomination
Step 4: choose one card from the remianing.
When they say denomination do they mean like:
A,2,3,4,5,6,7,8,9,10,J,Q,K
also why do they say choose 2 cards rfom the small and large denomination? couldn't u do it by getting like 2 kings, and 2 10's, and 1 other card like a 2?
These are all large denominations.
When i did this problem i thought it would be solved like this:
You have 52 cards to pick from, but you only want 2 denominations, so
Step 1: 52 choose 2
Step 2: You already used 2 cards so you only have 50 to choose from now, so 50 choose 2
Okay now you should have 4 cards, now you only need 1 more card, but you can't choose a card you picked in step 1 or 2, so u must take 52-4 = 48, 48 choose 2
(52 choose 2) * (50 choose 2) * (48 choose 1)
But they did it the following way:
total number of hands with two pairs:
Step 1: 13 choose 2
Step 2: 4 choose 2
step 3: 4 choose 2
step 4: 44 choose 1
i'm not sure how they got this...
Also the 44 choose 1, I am not sure how they got 44. Any explanation would be great!