Drawing five cards from a standard deck has how many possible outcomes and why?

Step-by-step explanation:

Lots, even if you make this a combination problem. I'm going to treat it as a permutation first and then we'll look into a combination.

52 P 5 is the same thing as a counting problem

The first card drawn is 1 of 52

The second one drawn is 1 of 51

The third one drawn is 1 of 50

The 4th one drawn is 1 of 49

The 5 one drawn is 1 of 48

The answer you should get is 311 875 200

If your calculator does this then you should put in 52P5 and it will give you the possible outcomes.  Remember the question asks you the number of outcomes not the probability.

The above number treats the order as different.

So 12345 is not the same as drawing 12354.

Those 2 sets of cards are counted as 2 not one.

I believe this to be the best answer.

But if order does not matter, and you want 1 2 3 4 5 to be the same thing as  1 2 3 5 4 the problem is a combination problem. Ignoring the suits the answer is

52 C 5

which is 52 * 51 * 50 * 49 * 48 / 5! = 2598960

I don't know how far into the course you are but the actual answer would have to account for the suits. This solution assumes that the actual card drawn remains upside down, that is, if it is the king of hearts, you don't know it.