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
- Family
What is the probability that a family with 3 children has: exactly 1 girl? 2 girls and 1 boys? Consider the birth probability of a girl as 48.66% and a boy as 51.34%. - Chords
How many 4-tones chords (chord = at the same time sounding different tones) is possible to play within 7 tones? - Subsets
How many 19 element subsets can be made from the 26 element set? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - Calculation of CN
Calculate: (486 choose 159) - (486 choose 327) - Hockey
The hockey match ended 8:10. How many different matches could be? - Count of triangles
On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
- Combinatorics
The city has 7 fountains. Works only 6. How many options are there that can squirt? - Intersection of the lines
How many points do nine lines intersect in a plane, of which four are parallel, and of the other five, no two are parallel (and if we assume that only two lines pass through each intersection)? - 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? - Divide
How many different ways can three people divide seven pears and five apples? - Cards
The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace - Points in plane
The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points? - First class
The shipment contains 40 items. 36 are first-grade, and four are defective. How many ways can we select five items so that it is no more than one defective? - Possibilities 5058
Adamko is two years old and does not want to clean his toys. One night, the toy fairy came to his room and saw legos, a police car, blocks, and a train lying on the floor. The fairy decided to take 3 toys from Adamko. How many choices does a trio of toys
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