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.)
Answer
The total number of possible 3-card poker hands is \(\boxed{22100}\).
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 \(\boxed{22100}\).
