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
- Examination
The class is 25 students. How many ways can we choose 5 students for examination? - Lines
How many points will intersect 27 different lines where no two are parallel? - Test - questions
You have a test with eight questions, where you can choose from 3 answers for each question, and one answer is always correct. The probability that we answer 5 or 6 questions correctly when randomly filling in (that is, we all guess the answers) is ……. Th - Numbers 7755
How many digits 7 are in numbers from 1 to 777? - Numbered
In the past, passengers in public transport vehicles marked such single-use tickets, which had 9 numbered boxes, a certain number of which were punched with a marker. A) In how many different ways could the ticket be marked if 3 boxes were punched? B) How - Designated 66594
Marenka is required to read three books out of five designated books. How many ways can three books choose to be read? - In the shipment
There are 40 products in the shipment. Of these, 4 are defective. In how many ways can we select 5 products so that exactly 3 of them are good?
- Three-digit numbers
How many three-digit numbers are from the numbers 0, 2, 4, 6 8 (with/without repetition)? - 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 - Points in space
There are n points, of which no three lie on one line and no four lies on one plane. How many planes can be guided by these points? How many planes are there if there are five times more than the given points? - Probability 38083
The police solved 21 crimes in the monitored period. The probability of solving a crime is 0.64. What is the probability that the police: a) just solved 7 crimes b) did not solve at least 2 criminal offenses P.S. Let's assume ideal police officers - Probability 81115
The probability of sprouting each avocado pit is 0.9. We planted 3 stones. What is the probability that exactly two of them will sprout? - Questions 81676
You will learn 50% of the 30 questions. If I get 4 questions, I'll know 3. - Green cards
We draw 4 cards from 32 cards. In how many ways can we draw a) exactly 2 aces, b) 3 green ones - Intersect 5216
At how many points do ten lines intersect if no two are parallel?
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