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
- 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? - Ribbons 6640
Danka knits a sweater and has a choice of seven colors. a) How many ways can he choose three colors for the sleeves? b) He wants ribbons of four colors on his back. How many options does he have to choose from? - Probability 80560
I have 3 sources, and their failure probability is 0.1. Calculate the probability that: a) none will have a malfunction b) 1 will have a breakdown c) at least 1 will have a fault d) they will all have a breakdown - A basket 4
A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges. - 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? - 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 - STRESSED word
Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled. - Sick days
In Canada, there are typically 261 working days per year. There is a 4.9% chance of an employee taking a sick day. What is the probability an employee will use 17 OR MORE sick days in a year? - Four-element combinations
How many four-element combinations can we make from 10 elements? - Manufacturer 24801
Five hundred of the products in the series are to be inspected with a repeat check. The manufacturer guarantees 2% scrap for a given production. Determine the probability of scraps among the 500 products reviewed between 12 and 20. - Tournament
How many matches will be played in a football tournament in which there are two groups of 5 teams if one match is played in groups with each other and the group winners play a match for the tournament's overall winner? - Ten persons
Ten persons, each person, make a hand to each person. How many hands were given? - Competition 33041
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? - Honored students
Of the 25 students in the class, ten are honored. How many ways can we choose five students from them if there are to be exactly two honors between them? - Students 36881
As a reward, the trip's land is ten students from a class of 25 students. How many options are there?
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