How many ways can you select 4 cards from a deck of 52 cards?

₹0.0

Question: How many ways can you select 4 cards from a deck of 52 cards?

Options:

Correct Answer: 270725

Solution:

The number of ways to select 4 cards from 52 is C(52, 4) = 270725.

How many ways can you select 4 cards from a deck of 52 cards?

How many ways can you select 4 cards from a deck of 52 cards?

Step 1: Understand that we want to select 4 cards from a total of 52 cards.
Step 2: Recognize that the order in which we select the cards does not matter. This means we will use combinations, not permutations.
Step 3: The formula for combinations is C(n, r) = 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 = 4 (cards to select).
Step 5: Plug the values into the formula: C(52, 4) = 52! / (4! * (52 - 4)!)
Step 6: Calculate 52! (the factorial of 52), 4! (the factorial of 4), and 48! (the factorial of 48).
Step 7: Simplify the expression: C(52, 4) = (52 * 51 * 50 * 49) / (4 * 3 * 2 * 1).
Step 8: Perform the multiplication in the numerator: 52 * 51 * 50 * 49 = 6497400.
Step 9: Perform the multiplication in the denominator: 4 * 3 * 2 * 1 = 24.
Step 10: Divide the results: 6497400 / 24 = 270725.
Step 11: Conclude that there are 270725 ways to select 4 cards from a deck of 52 cards.

Combinatorics – The study of counting, specifically how to choose items from a larger set without regard to the order of selection.
Binomial Coefficient – The formula C(n, k) = n! / (k!(n-k)!) used to calculate the number of ways to choose k items from n items.