In a deck of 52 cards, 3 cards are chosen. What is the probability that all three card are picture cards? (king, queen, jack)
By the way, we are learning combinations and permutations.
Help would be greatly appreciated!
There are four suits in each deck, each with 3 picture cards for a total of 12 picture cards in a deck of 52 (different) cards.
The probability of choosing r objects from a pool of n different objects is
C(n,r) = n! / ((n-r)!r!)
where n!=factorial n = n(n-1)(n-2)...3.2.1
For example,
6!=6*5*4*3*2*1=720
For better learning, you would do well doing some further reading on the subject, such as:
http://www.mathsisfun.com/combinatorics/combinations-permutations.html
is an easy reading.
Please remember, solving a problem without understanding the subject will not help you solve the next ones.
Can you please solve it for me?
Im still a bit confused...
Probability
=C(52,12)
Use your calculator function nCr to calculate C(52,12) where n=52, and r=12.
Or calculate
=52!/((52-12)!(12!))
=52!/(40!*12!)
You need to get familiar with these calculations if you are to learn anything from probabilities.
You have 12/52 for the first choice, 11/51 for the second and 10/50 for the third. Just multiply the three probabilities.
MathMate, your instructions are incorrect for the question asked.
C(52,12) is the number of combinations of 12 different cards that can be made from 52 cards.
Thank you GanonTEK!
Indeed, (12/52)(11/51)(10/50) is the correct answer. My bad!
To find the probability that all three cards are picture cards (king, queen, jack), you need to determine the number of favorable outcomes (the number of ways to choose three picture cards) and the total number of possible outcomes (the number of ways to choose any three cards).
Here's how you can calculate it step by step:
Step 1: Determine the number of favorable outcomes.
There are 4 picture cards in each suit (king, queen, jack), and since there are 4 suits in a standard deck, the total number of picture cards is 4 x 4 = 16. Now, you need to choose 3 picture cards from these 16.
To calculate this, you can use combinations since the order in which the picture cards are chosen does not matter. The formula for combinations is given by:
nCr = n! / [(n - r)! * r!]
where n is the total number of items and r is the number of items being chosen.
In this case, n = 16 (the total number of picture cards) and r = 3 (the number of picture cards being chosen).
So, the number of ways to choose 3 picture cards from 16 can be calculated as:
16C3 = 16! / [(16 - 3)! * 3!]
= 16! / (13! * 3!)
= (16 * 15 * 14) / (3 * 2 * 1)
= 560
Step 2: Determine the total number of possible outcomes.
When choosing 3 cards from a deck of 52 cards, we can use combinations again since the order in which the cards are chosen does not matter. The total number of possible outcomes can be calculated as:
52C3 = 52! / [(52 - 3)! * 3!]
= 52! / (49! * 3!)
= (52 * 51 * 50) / (3 * 2 * 1)
= 22,100
Step 3: Calculate the probability.
Finally, you can calculate 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
= 560 / 22,100
≈ 0.0253
So, the probability that all three chosen cards are picture cards is approximately 0.0253, or 2.53%.
I hope this explanation helps you understand how to approach probability problems involving combinations.