Combinations Calculator
The calculator finds the number of combinations of the k-th class from n elements without repetition. A combination without 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 repetition).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
- Topic probability
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? - 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? - From experience
Based on the experience of an insurance company employee, it was found that an insurance payout under household insurance exceeds 25,000 CZK with a probability of 0.3. What is the probability that among the next ten insurance claims: a) at least 5 will ex - Intersect of 10 lines
At how many points do ten lines intersect if no two are parallel? - Component fail
There is a 90 percent chance that a particular type of component will perform adequately under high-temperature conditions. If the device involved has four such components, determine the probability that the device is inoperable because precisely one of t - All use computer
It is reported that 72% of working women use computers at work. Choose three women at random, and find the probability that all three women use a computer in their jobs. - Probability of failures The probability of failure in specific productions is 0.01. Calculate the likelihood of more than one failure among the 100 selected products if we return them to the file after the check.
- Component deviation probability
There are 200 components in the production batch, of which 26 have a plus deviation from the nominal value. Calculate the probability that none of the 10 products selected will have a positive variance if we make selections without repetition - Alopecia
Medical literature indicates that 45% of men suffer from alopecia. For a random sample of 8 men, calculate the probability that: (a) exactly four men suffer from alopecia. (b) at most, two men suffer from alopecia. - Tournament match calculation
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? - Soccer teams
Have to organize soccer teams. There are three age groups. How many different ways can you organize ten teams for each age group? Is this a permutation or combination? - 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? - Seedbeds
The father wants to plant two seedbeds of carrots and two seedbeds of onion. Use a tree chart to find how many different options he has for placing the seedbeds. - Cart content options
We put seven different things out of fifteen various goods in the shopping cart. How many cart content options occur? - Machine defect probability
The machine produces one part in 2 minutes. The probability that it is defective is 0.05. What probability will the machine produce exactly ten defective parts per shift (8 hours)?
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