Two cards drawn, without replacement from standard deck 52 cards, how many sets of two cards are possible?

Answer 1

You have 52 choices for the first card and 51 for the second card, so it's 52*51 choices = 2652 choices

However, the above answer counts the Ace of Spades, followed by the King of Spades as one choice, and the King of Spades followed by the Ace of Spades as a different choice.

Ordinarily, we would call those two choices the same thing. To correct for that, divide the above answer by 2 = 1326 choices. But either answer is possible, depending on whether you wish to count a different order of the same cards as different or the same.

(For the record, the first answer is 52 P 2, and the second answer is 52 C 2)

Answer 2

The first answer is correct in both cases. The generic answer for permutations (P) is:

n!/(n-m)!

where n is the total and m is the number of samples you are taking. And the generic answer for combinations (C) is:

n!/(m! * (n-m)!)

In the "52 cards take 2" case, the permutations would be:

(52*51*50*49*...*2*1) / (50*49*...*2*1)

You'll notice that the denominator completely cancels out with the 50*49*... in the numerator, leaving 52 * 51 = 2652. And in the combinations case, the answer would be:

(52*51*50*49*...*2*1) / ((2*1)*(50*49*...*2*1))

Again, the 50*49*... cancels out, and you're left with (52*51)/2, or 26*51 = 1326.

Answer 3

Being the common card drawn it particularly is beside the ingredient what the 2d card would be. the probability continues to be 13 out of 50 two or 25% or one million in 4. The order of revealment performs no section, the common card drawn is and continuously could be the 1st card drawn from an entire % of 50 two enjoying cards. What the 2d card is is of no end result, it ought to be one extra spade yet we are informed that via utilising danger it became as quickly as now now not yet another spade.

Answer 4

With 52 cards there are 1326 (52c2) different combinations of cards that you can draw.