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
- Tournament match calculation
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe? - Student exam selection
V III. There are 22 students in the FPR class. How many ways can four students be selected for a DVK class exam? - Syrups
In the shop, they sell three types of syrups - apple, raspberry, and orange. How many ways can you buy four bottles of syrup? - Probability of picking
There are 5 chocolate, 3 cottage cheese, and 2 apricot croissants in the bag. Croissants are randomly selected in bags. What is the probability of drawing 1 chocolate, 1 cheese, and 1 apricot croissant without returning? - Pupil pair combinations
Without listing all the possibilities, calculate how many different pairs can be made A) of 12 pupils who want to go down a water slide on a two-seater inflatable in the water park. B) of 15 pupils who want to ride toy cars in the amusement park.
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