combinations from 2 hole card and 7 communal cards

If we have 5 communal cards and 2 hole cards, and its our turn to deal, Can we just select all the 5 communal cards for hand? or do we need to keep our 2 hole cards and only choose 3 communal cards out of 5 communal cards to make a hand?

Well, it's actually pretty easy. In Texas Hold'em you can combine them anyway you want. So the answer is yes, you can choose all the 5 community cards to form your hand1.

In fact, in Texas Hold'em, the total number of ways you can combine the cards is:

(7!) / ((5!) x (7 - 5)!) = (6 x 7) / 2! = (6 x 7) / 2 = 42 / 2 = 21.

where n! = n factorial = 1 x 2 x 3 ... x n

When it comes to Omaha (the only other poker variation that has community cards), things are a little more complicated, since you have additional restrictions (2 cards from your hand, 3 from the community cards, NO EXCEPTIONS). I'm not going to present the calculation in the case of Omaha here (it's a bit longer), but if you're curious the result is 60.

1 = you probably lost the hand at that point, I suggest bluffing :D

• there are actually a lot of poker variations besides TH and Omaha that uses community cards, although maybe those are the only two which are in widespread use in casinos...
– user1934
Commented Mar 13, 2017 at 3:34
• @Michael Except for texas-holdem, omaha, omaha-hi-lo and recently 5-card-omaha, I've never heard of any other such variations. And I bet 99.9% of players are in the same situation. Commented Mar 13, 2017 at 8:45