Problem
A hand consists of 3 cards from a well-shuffled deck of 52 cards. a. Find the total number of possible 3 -card poker hands. b. A club flush is a 3-card hand consisting of all club cards. Find the number of possible club flushes. c. Find the probability of being dealt a club flush. a. There are a total of poker hands. b. There are possible club flushes. c. The probability is (Type an integer or decimal rounded to six decimal places as needed.)
Solution
Step 1 ：Use the combination formula: C(n, k) = n! / [k!(n-k)!], where n is the total number of items, k is the number of items to choose, and '!' denotes factorial.
Step 2 ：Substitute n=52 (total number of cards) and k=3 (number of cards to choose) into the formula.
Step 3 ：Calculate the factorial of n, k, and (n-k).
Step 4 ：Divide the factorial of n by the product of the factorial of k and the factorial of (n-k).
Step 5 ：The total number of possible 3-card poker hands is \(\boxed{22100}\).
