N Choose K Calculator
Find out how many different ways you can choose k items from n items set without repetition and without order. This number is also called combination number or n choose k or binomial coefficient or simply combinations. See also general combinatorial calculator.Calculation:
Ck(n)=(kn)=k!(n−k)!n! n=10 k=4 C4(10)=(410)=4!(10−4)!10!=4⋅3⋅2⋅110⋅9⋅8⋅7=210
The number of combinations: 210
A bit of theory - the foundation of combinatorics
Combinations
A combination of the k-th class of n elements is an unordered k-element group formed from a set of n elements. The elements are not repeated and the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:Ck(n)=(kn)=k!(n−k)!n!
A typical example: we have 15 students and need to choose 3. How many ways can this be done?
Foundation of combinatorics in word problems
- Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - Event probability
The probability of event N in 5 independent experiments is 0.4. What is the probability that the event N occurs in one experiment (chance is the same)? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - Rectangle
In a rectangle with sides, 8 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than any side of the rectangle? - 7 heroes
6 heroes galloping on 6 horses behind. How many ways can we sort them behind? - Count of triangles
On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points. - Cars plates
How many different license plates can a country have since they use 3 letters followed by 2 digits? - Ace
We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace? - Circles
How many different circles are determined by 14 points at the plane if 3 of them lie in a straight line? - Hockey players
After we cycle, five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other? - Olympics
How many ways can six athletes be placed on the podium at the Olympics? Depends on the color of the metal. - Hockey match
The hockey match ended with a result of 3:1. How many different storylines may the match have? - Five-digit
Find all five-digit numbers that can be created from number 12345 so that the numbers are not repeated and then numbers with repeated digits. Give the calculation. - Hockey game
In the hockey game, they scored six goals. The Czechs played against Finland. The Czechs won 4:2. In what order did they fall goals? How many game sequences were possible during the game? - Ten dices
When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
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