N Choose K Calculator n=12, k=2 result

Find out how many different ways you can choose k items from a set of n items 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.

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

• Chords
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• Rectangle
  In a rectangle with sides 8 and 9, a diagonal is drawn. What is the probability that a randomly selected point inside the rectangle is closer to the diagonal than to any side of the rectangle?
• No. of divisors
  How many different divisors have number 13 ⁴ * 2 ⁴?
• Cards
  How many ways can you give away 32 playing cards to 4 player?
• Chambers
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• Three digits number 2
  Find all three-digit positive integers that can be formed from the digits 1, 2, 3, and 4, subject to the following conditions: the units digit is one of 1, 3, or 4, and the hundreds digit is 4 or 2.
• Eight blocks
  Dana had the task of saving the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be fo
• Cards
  The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace
• Divisible by five
  How many different three-digit numbers divisible by five can we create from the digits 2, 4, and 5? We can repeat the digits in the created number.
• Tricolors
  From the colors - red, blue, green, black, and white, create all possible tricolors.
• Three-digit numbers
  How many different three-digit natural numbers can be created so that the digits are different and the last digit is 0?
• Dice
  We threw ten times playing dice. What is the probability that the six will fall exactly four times?
• Utopia Island
  The probability of disease A on the island of Utopia is 40%. The probability of occurrence among the men of this island, which make up 60% of all the population (the rest are women), is 50%. What is the probability of occurrence of A disease among women o
• Two Digit Numbers Digits
  How many two-digit numbers can be written using the number 0,2,6? We can also repeat the digits in the number.
• Bus route network
  A new bus route network was built. There are three stops on each line. In addition, every two lines either do not have a common stop or have only one common stop. What is the largest number of tracks there can be in a town if we know there are only nine d

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