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 a 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 it does not matter the order of the group's elements. In mathematics, disordered groups are called sets and subsets. Their number is a combination number and is calculated as follows:Ck(n)=(kn)=k!(n−k)!n!
A typical example of combinations is that we have 15 students and we have to choose three. How many will there be?
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 3 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 11 points at the plane if 7 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?
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?more math problems »
