n choose k calculator n=100, k=10 result
Find out how many different ways you can choose k items from n items set without repetition and without order. This number is also called combination number or n choose k or binomial coefficient or simply combinations. See also general combinatorial calculator.Calculation:
Ck(n)=(kn)=k!(n−k)!n! n=100 k=10 C10(100)=(10100)=10!(100−10)!100!=17310309456440
The number of combinations: 17310309456440
17310309456440
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
- Trinity
How many different triads can be selected from group 38 students? - 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? - Determine 79604
In the shoe cabinet, there is one pair each of boots, sandals, tennis shoes, and brown and black ankle boots. Determine how many ways one right shoe and one left shoe can be chosen from among them that do not belong together. - Different 68754
We have six balls of different colors. We select two balls at once. How many options?
- Disco
At the disco goes 12 boys and 15 girls. In how many ways can we select four dancing couples? - Five brown
Five brown eye contracts, seven green pairs, and four blue pairs. What's the probability Gianna will randomly select a brown or green pair? - Sons
The father has six sons and ten identical, indistinguishable balls. How many ways can he give the balls to his sons if everyone gets at least one? - Percentages 83188
There are 10 bags displayed in the store, 2 of which have a hidden error. Buyers randomly choose one bag. Express in percentages the probability that they will buy the bag without a mistake. - Choices 82334
There are 15 black and 15 white balls in an opaque bag. Elenka took one ball out of the bag three times. what choices of the three balls could she choose?
- Probability 3080
There are eight styles of graduation topics in the Slovak language. The Minister of Education draws 4 of them. What is the probability that he will choose at least one of the pairs? - Weekly service
In the class are 20 pupils. How many opportunities has the teacher selected for two pupils who will have a week-class service randomly? - Three coins
In a game of chance where three coins are tossed, a player wins if two heads and a tail come up. What are the chances of this occurring? - Three-part novel
In how many ways can seven books be stored on a shelf if there is one three-part novel to be placed side by side? - Tournament
Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other?
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