n choose k calculator n=112, k=3 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=112 k=3 C3(112)=(3112)=3!(112−3)!112!=3⋅2⋅1112⋅111⋅110=227920
The number of combinations: 227920
227920
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
- Representative 81580
The chess club has 5 members, including two girls. The circle leader wants to determine by lot which member will represent the circle at the representative tournament. What is the probability that a girl will be drawn? - Simultaneously 80530
The product has a 10% probability of an appearance defect, a 6% probability of a functional deficiency, and a 3% probability of both defects simultaneously. Are the random events A - the product has an appearance defect and B - the product has a functiona - Playmakers 83340
In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game? - The probability 2
The probability that an adult possesses a credit card is 0.71. A researcher selects two adults at random. The probability (rounded to three decimal places) that the first adult possesses a credit card and the second adult does not possess a credit card is
- Probability 1775
The company has so far produced 500,000 cars, of which 5,000 were defective. What is the probability that at most one car out of daily production of 50 cars will be defective? - Menu
On the menu are 12 kinds of meals. How many ways can we choose four different meals for the daily menu? - Medals
How many ways can gold, silver, and bronze medals be divided among 21 contestants? - 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? - First man
What is the likelihood of a random event where are five men and seven women will first leave the man?
- Tokens
The non-transparent bags are red, white, yellow, and blue tokens. We 3times pulled one token and again returned it, writing down all possibilities. - Olympics metals
How many ways can one win six athletes' medal positions in the Olympics? Metal color matters. - Metals
In the Hockey World Cup, play eight teams, and determine how many ways they can win gold, silver, and bronze medals. - 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 - Probability 80860
During the exam, the student takes 3 questions out of 20. He is ready for 14 of them. Find the probability that he draws at least one that he knows.
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