To determine how many 4 card hands can be formed from a standard 52 card deck, we need to use the concept of combinations. In mathematical terms, a combination is a way of selecting items from a larger pool where the order does not matter.
The formula for combinations is given by:
C(n, r) = n! / (r! * (n – r)!)
In this case, n is the total number of cards in the deck (52), and r is the number of cards we want to select (4). Applying the formula:
C(52, 4) = 52! / (4! * (52 – 4)!)
This simplifies to:
C(52, 4) = 52! / (4! * 48!)
We can cancel out the factorials:
C(52, 4) = (52 × 51 × 50 × 49) / (4 × 3 × 2 × 1)
Now calculating this gives us:
C(52, 4) = 270725
Thus, there are a total of 270,725 possible 4 card hands that can be formed from a standard 52 card deck.