How many possible distinct 5 card hands can be dealt from a standard 52 card deck? The order in which the cards are dealt doesn't matter.

I know it ISN'T 52 choose 5 because the cards have to be DISTINCT, or DIFFERENT.

what you say you know is incorrect

all 52 cards in a deck are different

To determine the number of possible distinct 5-card hands from a standard 52-card deck, you can use the concept of combinations.

Since the order in which the cards are dealt doesn't matter, we can use the combination formula. The number of combinations of n items taken r at a time is given by the formula: nCr = n! / (r!(n-r)!), where n! represents n factorial.

In this case, we have a deck of 52 cards, and we want to select 5 cards, so n = 52 and r = 5.

Calculating the number of possible combinations:

52C5 = 52! / (5!(52-5)!)
= 52! / (5!47!)
= (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
= (311,875,200) / (120)
= 2,598,960

Therefore, there are 2,598,960 possible distinct 5-card hands that can be dealt from a standard 52-card deck.

To find the number of possible distinct 5-card hands from a standard 52-card deck, we need to use the concept of combinations.

First, we need to understand that when it comes to combinations, the order of the cards does not matter. So, we need to use the formula for combinations, which is " n choose r", denoted as nCr.

In this case, we have 52 cards in the deck, and we want to choose 5 cards without considering the order. So, we can calculate it as:

52C5 = 52! / (5! * (52-5)!)

Let's break down the calculation step by step:

1. Calculate the factorial of 52: 52! = 52 x 51 x 50 x 49 x ... x 1
2. Calculate the factorial of 5: 5! = 5 x 4 x 3 x 2 x 1
3. Calculate the factorial of (52-5): (52-5)! = 47 x 46 x ... x 1
4. Divide 52! by (5! * (52-5)!) to get the number of combinations.

Now, let's calculate it:

52C5 = 52! / (5! * (52-5)!)
= (52 x 51 x 50 x 49 x ... x 1) / (5 x 4 x 3 x 2 x 1 x (47 x 46 x ... x 1))
= (2598960) / (120 × 47 × 46 × 45 × 44)
≈ 2,598,960

Therefore, there are approximately 2,598,960 possible distinct 5-card hands that can be dealt from a standard 52-card deck.

It is C(52,5), trust us

another approach:
suppose you had to pick them in a specific order,
then the number of ways would be 52x51x50x49x48
which is the same as 52! / 47! or P(52,5)
But the order does not matter, as you said, so we have to divide by 5! the number of arrangements that would all yield the same selection
thus getting 52!/47! ÷ 5! , which is 52!/(47!5!) = C(52,5) by definition.