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).

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

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:

$C_k(n)=\left(\genfrac{}{}{0ex}{}{n}{k}\right)=\frac{n!}{k!(n-k)!}$

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

• Examination
  The class is 25 students. How many ways can we choose 5 students for examination?
• Bulb lifespan
  The probability that the bulb will burn for more than 800 hours is 0.2. There are 3 light bulbs in the hallway. What is the probability that after 800 hours, at least one will be lit?
• The confectionery
  The confectionery sold five kinds of ice cream. If the order of ice cream does not matter, how many ways can I buy three kinds?
• Ice cream
  Annie likes ice cream. In the shop are six kinds of ice cream. How many ways can she buy ice cream in three scoops if each has a different flavor mound and the order of scoops doesn't matter?
• Goal divisions
  School players scored seven goals in the match. List all possible goal divisions into three-thirds and add up how many.
• Two aces
  From a 32-card box, we randomly pick 1 card and then two more cards. What is the probability that the last two drawn cards are aces?
• First class
  The shipment contains 40 items. 36 are first-grade, and four are defective. How many ways can we select five items so that it is no more than one defective?
• 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
• Sum or product
  What is the probability that two dice fall will have the sum of seven or product 12?
• Dice
  We threw ten times playing dice. What is the probability that the six will fall exactly four times?
• Peaches
  There are 20 peaches in the pocket. Three peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten?
• Triplets From Four Pupils
  How many different triplets can be created from 4 pupils if it does not matter the order of the pupils in the triplets?
• Card selection ways
  How many ways do we know to select three cards from a deck of seven cards so that there are two red and one green between them?
• Weekly student selection
  There are 16 students in the class. If the teacher wants to choose two students who will be weekly, how many options does she have?
• Employee sample probability
  Out of 3,000 employees of a certain company, 1,800 are men. The management decided that on the occasion of the company's anniversary celebration, it will give special rewards to 10 randomly drawn employees. What is the probability that the sample will be

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