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).

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

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:

$C_k(n)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\frac{n!}{k!(n-k)!}$

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?
• 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)?
• 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 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?
• 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
• 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)?
• Ten persons
  Ten persons, each person, make a hand to each person. How many hands were given?
• Doesn't 37531
  How many ways can you draw eight playing cards from 32 playing cards when their order doesn't matter?
• 9 rectangles
  A large rectangle is divided into 9 small rectangles. How many rectangles are there in total?
• Probability 3080
  There are eight styles of graduation topics in the Slovak language. The Minister of Education draws 4 of them. How likely is he to choose at least one of the pairs?
• Diagonals
  What x-gon has 54 diagonals?
• Opportunities 8372
  There are 20 students in the class, four of them are being tested by the teacher. How many options are there to choose who the teacher will test?

more math problems »