Five cards are drawn from a standard deck, what is the probability of picking 3 face cards?
To find the probability of picking 3 face cards out of 5 cards drawn from a standard deck, we need to calculate two things:
1. The total number of possible outcomes: This is the number of ways we can choose any 5 cards out of the 52 cards in a standard deck. We can calculate this using the combination formula, denoted as "nCr", where "n" is the total number of items and "r" is the number of items we are choosing. In this case, it would be 52C5, which equals:
52C5 = 52! / (5! * (52-5)!)
2. The number of favorable outcomes: This is the number of ways we can choose 3 face cards out of the 12 face cards in the deck, along with 2 other non-face cards. We can calculate this using another combination formula:
12C3 * 40C2 = (12! / (3! * (12-3)!) ) * (40! / (2! * (40-2)!))
After calculating these two values, we can find the probability by dividing the number of favorable outcomes by the total number of possible outcomes:
Probability = Number of favorable outcomes / Total number of possible outcomes
Let's calculate this step by step:
Total number of possible outcomes:
52C5 = 52! / (5! * (52-5)!)
Number of favorable outcomes:
(12! / (3! * (12-3)!) ) * (40! / (2! * (40-2)!))
Then, divide the number of favorable outcomes by the total number of possible outcomes to get the probability.