From a deck of 52 cards, how many ways can you choose 5 cards?

From a deck of 52 cards, how many ways can you choose 5 cards?

Step 1: Understand that we want to choose 5 cards from a total of 52 cards.
Step 2: Recognize that the order in which we choose the cards does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is given by nCr = n! / (r! * (n - r)!), where n is the total number of items, r is the number of items to choose, and '!' denotes factorial.
Step 4: In our case, n = 52 (total cards) and r = 5 (cards to choose).
Step 5: Calculate 52C5 using the formula: 52C5 = 52! / (5! * (52 - 5)!)
Step 6: Simplify the calculation: 52C5 = 52! / (5! * 47!) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
Step 7: Perform the multiplication for the numerator: 52 * 51 * 50 * 49 * 48 = 311875200.
Step 8: Perform the multiplication for the denominator: 5 * 4 * 3 * 2 * 1 = 120.
Step 9: Divide the numerator by the denominator: 311875200 / 120 = 2598960.
Step 10: Conclude that there are 2598960 ways to choose 5 cards from a deck of 52 cards.

Combinatorics – The question tests the understanding of combinations, specifically how to calculate the number of ways to choose a subset of items from a larger set without regard to the order of selection.