N Choose K Calculator n=5, k=3 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

• Chess
  How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
• Rectangles
  How many rectangles with an area of 8855 cm² have sides that are natural numbers?
• Pizza
  A school survey found that 10 out of 15 students like pizza. If 5 students are chosen randomly, what is the probability that all 5 students like pizza?
• Count of triangles
  On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
• Probabilities
  If probabilities of A, B, and A ∩ B are P (A) = 0.62, P (B) = 0.78, and P (A ∩ B) = 0.26, calculate the following probability (of the union. intersect and opposite and its combinations):
• Combinatorics
  The city has 7 fountains. Works only 6. How many options are there that can squirt?
• Chess
  How many different ways can you initiate a game of chess (first pass)?
• Three digits number
  From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there?
• Intersection of the lines
  How many points do nine lines intersect in a plane, of which four are parallel, and of the other five, no two are parallel (and if we assume that only two lines pass through each intersection)?
• Medicine
  We test medicine on six patients. For all, the drug doesn't work. If the drug success rate of 20%, what is the probability that medicine does not work?
• 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
• Permutations without repetition
  From how many elements can we create 720 permutations without repetition?
• Two-digit numbers
  Write all the two-digit numbers that can be composed of the digit 7,8,9 without repeating the digits. Which ones are divisible b) two, c) three d) six?
• Points in plane
  The plane is given 12 points, 5 of which are located on a straight line. How many different lines could be drawn from these points?
• Three-digit code
  The five cards with the numbers 1, 2, 3, 4, and 5 put together all three-digit odd numbers. How many are there?

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