Question

You are dealt a hand of 5 cards from a standard deck of 52 cards. Find the probablity of being dealt two clubs and three cards with one card of each other remaining suit. The probability is ________(Round to six decimal places as needed.)

Answer 1

The probability of being dealt two clubs and three cards with one card of each other remaining suit is 2.75%.

Step-by-step explanation:

To find the probability of being dealt two clubs and three cards with one card of each other remaining suit, we need to consider the total number of ways this can occur and divide it by the total number of possible outcomes.

Step 1: Calculate the number of ways to choose two clubs from the 13 clubs in the deck: C(13, 2) = 78

Step 2: Calculate the number of ways to choose three cards with one card of each other remaining suit from the 39 cards in the other three suits: C(39, 3) = 9139

Step 3: Calculate the total number of ways to choose 5 cards from the 52 cards in the deck: C(52, 5) = 259,896

Step 4: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes: 78 * 9139 / 259,896 = 2.75%