Five cards are drawn from a standard deck, what is the probability of picking 3 face cards?
prob = C(12,3) x C(40,2)/C(52,5)
= 220(780)/2598960
= 55/833 or appr .066
Thanks alot! Could you possibly elaborate as to how you approach this type of problem?
To find the probability of picking 3 face cards from a standard deck of 52 cards, we need to determine the number of favorable outcomes (picking 3 face cards) and the total number of possible outcomes (drawing any 5 cards from the deck).
Step 1: Find the number of favorable outcomes.
In a standard deck, there are 12 face cards (4 Jacks, 4 Queens, and 4 Kings). To choose 3 face cards, we can think of it as selecting 3 out of the 12 total face cards. This can be calculated using the combination formula, written as C(n, r), where n is the total number of items and r is the number of items chosen. In our case, n = 12 (total face cards) and r = 3 (number of face cards to choose).
Using the combination formula, the number of ways to choose 3 face cards from 12 is:
C(12, 3) = 12! / (3! * (12 - 3)!) = 220
So, there are 220 different ways to select 3 face cards from a deck.
Step 2: Find the total number of possible outcomes.
When drawing 5 cards from a standard deck, the total number of possible outcomes can be calculated as C(52, 5) because we are choosing any 5 cards from the 52-card deck.
Using the combination formula, the total number of ways to choose 5 cards from 52 is:
C(52, 5) = 52! / (5! * (52 - 5)!) = 2,598,960
Therefore, there are 2,598,960 different ways to draw 5 cards from a standard deck.
Step 3: Calculate the probability.
The probability of picking 3 face cards can be found by dividing the number of favorable outcomes by the total number of possible outcomes.
Probability = Number of favorable outcomes / Total number of possible outcomes
Probability = 220 / 2,598,960
Simplifying this fraction gives us the final probability:
Probability = 1 / 11,809
So, the probability of picking 3 face cards when drawing 5 cards from a standard deck is approximately 0.00008454 (rounded to 5 decimal places), or 0.008454% (rounded to 3 decimal places).