- #1

mr_coffee

- 1,629

- 1

This is suppose to be on how many ways can a certain hand be constructed.

**b: A**

9 ways (from A, 2, 3, 4, 5, 6, 6, 8 or 9, but not 10, since 10 J Q K A is a royal flush, not a straight flush). So

there are 36 straight flushes.

__straight flush__can be constructed by choosing a suit in 4 ways, and choosing the lowest denomination in9 ways (from A, 2, 3, 4, 5, 6, 6, 8 or 9, but not 10, since 10 J Q K A is a royal flush, not a straight flush). So

there are 36 straight flushes.

It doesn't look like he even used combinations in this but just applied the muliplciation rule, but this confusees me more because your "choosing" out of a hand so why not use combinations?

I would have thought it would have worked like this:

Step 1: Choose the suit

Step 2: Choose the denominations in that suit

An example of a straight flush is this:

Q♠ J♠ 10♠ 9♠ 8♠

but in this problem he says, but not 10. but clearly it can be constructed if you use the 10 card and you still won't end up with a royal flush.

another example would be:

7♥ 6♥ 5♥ 4♥ 3♥

Okay so Step 1: There are 4 suits total, you only need to pick 1 suit, and stick with that suit. So 4 choose 1.

Step 2: You need to now pick 5 cards of that suit, so you only have 13 choices, so (13 choose 5)

I get: (13 choose 5) * (4 choose 1) = 5148

If i restrict the card chocie to only the cards he said, that would be

A, 2, 3, 4, 5, 6, 6, 8 or 9

So another version i would get:

9 choose 5 * 4 choose 1 = 504, still not close to his answer.

If you can tell me the steps he used that would help, rather tahn my version where I said:

Step 1: Choose the suit

Step 2: Choose the denominations in that suit

-----------

**d:**

ways, and choosing another denomination and 2 cards of that denomination in 12 x (4 choose 2) = 72. so there are 52 x 72 = 3744 Full hosues

__A full house__can be constructed by choosing a denomination and 3 cards of that denomination in 13x4 = 52ways, and choosing another denomination and 2 cards of that denomination in 12 x (4 choose 2) = 72. so there are 52 x 72 = 3744 Full hosues

an example of a full house is the following:

3♣ 3♠ 3♦ 6♣ 6♥

So here is what I thought you would do:

Step 1: Choose a denomination

Step 2: Choose 3 cards of that denomination

Step 3: Choose another denomination

Step 4: choose 2 cards from that denomination

So..

Step 1: You have (52 choose 1), because you have 52 cards to choose from.

Step 2: Now that you already chose your denomination, you must select 3 cards of that type, but you already picked 1, so now you have 2 chocies left. soo (4 choose 2)

Step 3: Choose another denomination that wasn't the one you picked in step 1, so you have (51 choose 1) or would it be (52-3 choose 1), because you already picked 3 cards? so your left with 49 cards, so maye its (49 choose 1)

Step 4: You already picked 1 denomination, so you only need 1 more so you have 3 choose 1