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
- Combinatorics
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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?
- Effectiveness 80811
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On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points. - 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 - Rectangles
How many rectangles with area 3152 cm² whose sides are natural numbers? - Designated 64234
Marenka is required to read three books out of five designated books. How many ways can three books choose to be read?
- Five identical
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In a California community college, 60% of students will transfer to a college in the CSU system. The number of students in a sample who will transfer follows a binomial distribution. If eight students are randomly selected, find the population variance σ² - Hazard game
In the Sportka hazard game, six numbers out of 49 are drawn. What is the probability that we will win: a) second prize (we guess five numbers correctly) b) the third prize (we guess four numbers correctly)? - Prize
How many ways can 9 participants be rewarded with the first, second, and third prizes in a sports competition? - Questions 81676
You will learn 50% of the 30 questions. If I get 4 questions, I'll know 3.
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