Combinations calculator
The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination with repetition of k objects from n is a way of selecting k objects from a list of n. The order of selection does not matter and each object can be selected once (without repeated).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
- Tournament
Determine how many ways can be chosen two representatives from 34 students to school tournament. - Sales
From statistics of sales goods, item A buys 57% of people, and item B buys 76% of people. What is the probability that from 18 people buy 10 item A and 8 item B? - Rectangles
How many rectangles with area 3152 cm² whose sides are natural numbers? - Count of triangles
On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
- Circles
How many different circles are determined by 11 points at the plane if 7 of them lie in a straight line? - Hockey match
The hockey match ended with a result of 3:1. How many different storylines may the match have? - 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? - Class pairs
In a class of 34 students, including 14 boys and 20 girls. How many couples (heterosexual, boy-girl) can we create? By what formula? - Probability 2955
There are 18 girls and 13 boys in the class. Four pupils will be chosen by lot to supervise the breaks. What is the probability that it will be the boys themselves?
- Prize
How many ways can 9 participants be rewarded with the first, second, and third prizes in a sports competition? - Probability 3065
Natural numbers 4,5,7,11,12 are given. Calculate the probability of the event that the sum of three randomly selected numbers is less than 22. - Probability 3080
There are eight styles of graduation topics in the Slovak language. The Minister of Education draws 4 of them. How likely is he to choose at least one of the pairs? - Determined 3570
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points? - VCP equation
Solve the following equation with variations, combinations, and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0
Find the term independent of x in the expansion of (4x³+1/2x)8more math problems »
