Question

A flush in a five-card poker hand is five cards of the same suit. The suits are spades, clubs, diamonds and hearts. How many spade flushes are possible in a 52-card deck

Answer 1

There are 1,287 possible spade flushes in a 52-card deck, calculated using the combination formula for selecting five cards from the 13 available spades.

Step-by-step explanation:

To calculate the number of spade flushes possible in a 52-card deck, you need to select five cards from the 13 spades available in the deck. The formula for combinations (since order does not matter in poker hands) is used: C(n, k) = n! / (k!(n - k)!), where n is the total number of available cards in the suit, and k is the number of cards we want to select.

In this case, n = 13 (since there are 13 spades) and k = 5 (since we want a five-card flush). Plugging into the formula:

C(13, 5) = 13! / (5! * (13 - 5)!) = 13! / (5! * 8!) = (13 * 12 * 11 * 10 * 9) / (5 * 4 * 3 * 2 * 1) = 1287.

Therefore, there are 1,287 possible spade flushes in a 52-card deck when dealing with just spades.