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 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
- Lines
How many points will intersect 27 different lines where no two are parallel? - Trinity - triads
How many different triads can be selected from group 36 students? - Ticket code combinations
Tickets have 9 numbered windows. How many different codes can be set for each other if 3 or 4 windows are punched? - Plane count
There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points? - Dice
We threw ten times playing dice. What is the probability that the six will fall exactly four times? - 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. - Deficiencies
The hygienic inspection of 2000 mass caterers found deficiencies in 300 establishments. What is the probability that flaws in a maximum of 3 devices will be found during the inspection of 10 devices? - Point line determination
How many lines are determined by 5 points if three lie in one line? - Team formation ways
Determine how many ways it is possible to form a four-member team from 6 men and four women, where there are exactly two men. - Scrap probability
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. - Covid-19
Data showed that 22% of people in a small town were infected with the COVID-19 virus. A random sample of six residents from this town was selected. Find the probability that exactly two of these residents were infected. - Lotto ticket jackpot
Determine how many different ways a Lotto ticket can be written if we guess six numbers out of 49. At what Jackpot would it already pay to bet so many tickets to be guaranteed to win the 1st prize? The price of one type is €1. - Bridge cards
Determine the probability of a random event out of 10 randomly selected bridge cards. There will be at least three aces. Note This is a team game, with 52 cards in the deck, of which four aces. - Ball selection options
We have six balls of different colors. We select two balls at once. How many options? - From experience
From the experience of an insurance company employee, it turned out that the insurance benefit under household insurance is more than 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims there will be: a)
more math problems »
