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
- Rectangles
How many rectangles with area 8855 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. - 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)? - 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? - Cancel fractions
Compress the expression of factorial: (n+6)!/(n+4)!-n!/(n-2)! - Three students
Three students independently try to solve the problem. The first student will solve a similar problem with a probability of 0.6, the second student will solve at a probability of 0.55, and the third will solve at a probability of 0.04. The problem is reso - Guaranteed 37611
Determine how many different ways a Lotto ticket can be written if we guess six numbers out of 49. At what Jackpot would it already pay to bet so many tickets to be guaranteed to win the 1st prize? The price of one type is €1. - Effectiveness 80811
According to clinical studies, the effectiveness of the drug is 90%. The doctor prescribed the medicine to eight patients. What is the probability that the drug will be effective in all these patients? - Grouping - combinatorics
In how many different ways can 24 people be divided into: a) 6 groups of the same size. b) Groups of 5, 6, 7, and 6 people. c) Groups of 4, 5, 7, and 8 people. - The camp
At the end of the camp, a 6 friends exchanged addresses. Any friend gave their remaining 5 friends their card. How many addresses did they exchange? - Prize
How many ways can 9 participants be rewarded with the first, second, and third prizes in a sports competition? - Probability 3322
We have the numbers 4, 6, 8, 10, and 12. What is the probability that with a randomly selected triangle, these will be the lengths of the sides of a scalene triangle? - Probability 3349
We have natural numbers 3, 4, 6, 10, and 12. Calculate the probability that the sum of three randomly selected three different numbers is less than 20. - Triangles
Five sticks with a length of 2,3,4,5,6 cm. How many ways can you choose three sticks to form three sides of a triangle?
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