from a standard deck of 52 cards, how many different five-card hands can be drawn?
what is C(52,5) ?
To find the number of different five-card hands that can be drawn from a standard deck of 52 cards, we can use the concept of combinations.
The number of combinations of choosing k items from a set of n items, without considering the order, is given by the formula:
C(n, k) = n! / (k! * (n - k)!)
Here, we have 52 cards in the deck, and we want to choose 5 cards for our hand. Therefore, the number of different five-card hands can be calculated as:
C(52, 5) = 52! / (5! * (52 - 5)!)
Simplifying this expression:
C(52, 5) = (52 * 51 * 50 * 49 * 48) / (5 * 4 * 3 * 2 * 1)
Calculating the numerator:
52 * 51 * 50 * 49 * 48 = 311,875,200
Calculating the denominator:
5 * 4 * 3 * 2 * 1 = 120
Dividing the numerator by the denominator:
311,875,200 / 120 = 2,598,96
Therefore, there are 2,598,960 different five-card hands that can be drawn from a standard deck of 52 cards.