Combinations Calculator
The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination without 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 repetition).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 the 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 the order does not matter. In mathematics, such unordered groups are called sets and subsets. The count is called a combination number and is calculated as follows:Ck(n)=(kn)=k!(n−k)!n!
A typical example: we have 15 students and need to choose 3. How many ways can this be done?
Foundation of combinatorics in word problems
- Rectangles
How many rectangles with an area of 8855 cm² have sides that 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? - Running track
To the Akčesú races there came 25 runners. The running track was however narrow, and therefore always only five runners could run at once. What surprised Sára and Arthur the most however was the fact that the Te-TiVá people do not have stopwatches, nor ot - Test 10 questions
A test has 10 questions with multiple-choice answers. For the choice of the correct answer there are four options A, B, C, D, where always one of them is correct. How many are there all different possibilities for answers in this test, a) if its taker ans - Lotto ticket jackpot
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. - Drug effectiveness probability
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 a camp, 6 friends exchanged address cards. Each friend gave their card to each of the other 5 friends. How many cards were exchanged in total? - Triangle probability
From the numbers 4, 6, 8, 10, and 12, three are chosen at random. What is the probability that the three chosen numbers can form the sides of a scalene triangle? - 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? - Population variance
60% of students at a California community college 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 - Ten persons
Ten persons, each person, make a hand to each person. How many hands were given?
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