how many 5 card hands can be dealt from a standard deck of 52 cards is this permutation or combination?

Answer 1

This is a combination. There's a number of ways of thinking about it. This is the way I like to use:

Normally, if you were finding the odds of something, you would multiply the number of possibilities. The chance of a specific card out of 52 is 1/52, and since the deck now has one less it would be 1/51, and so on. So number of possible combinations is going to be like a factorial, but only iterated based on the number of draws. In this case:

52 x 51 x 50 x 49 x 48

Sometimes you'll see this in formulas as 52! / 47! (or n! / (n-k)!)which is the same thing, if you think about it.

When the order in which you draw the cards doesn't make a difference, there are obviously LESS possible combinations than there were before. This follows a similar pattern: the first card could have been in five spots, the second in four, and so on.

5 x 4 x 3 x 2 x 1

Or 5! (duh, I guess). You don't subtact this from the total number of permutations, you divide it, because each possible combination of hands has these possible 'duplicate' hands that we want to weed out from the total. So you have:

52 x 51 x 50 x 49 x 48
----------------------------
5 x 4 x 3 x 2 x 1

It has the same amount of numbers on the top as the bottom - the number of cards you drew. And the first number on top is the number of different answers (cards, in this case) and the last number on bottom is always one. That makes the whole thing easy to remember!

If you do the multipliction, you'll find that this works out to 2,598,959.5 possible combinations of first hands altogether. Hope that helps!

Answer 2

In dealing hands you are not interested in the order in which you get the cards, so it is a COMBINATION.

The number of combinations is 52 C 5, which is equal to
52! / (47! 5!), that is
(52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1) =
52 * 51 * 10 * 49 * 2 = 2,598,960

Answer 3

Card Hands

Answer 4

The order of arrangement does NOT matter in a card hand, so we have a combination problem.
The 52 cards may be combined into more than 2.5 million five-card hands.

Answer 5

52p5
this is permutation

Answer 6

it is combination
no of hands=52C5

Answer 7

please see the answer to your other question...

here, the order is not important.... so combination