N Choose K Calculator n=111, k=10 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

• Rectangles
  How many rectangles with an area of 8855 cm² have sides that are natural numbers?
• Count of triangles
  On each side of an ABCD square is 10 internal points. Determine the number of triangles with vertices at these points.
• Cars plates
  How many different license plates can a country have since they use 3 letters followed by 2 digits?
• Ace
  We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace?
• Hockey game
  In the hockey game, they scored six goals. The Czechs played against Finland. The Czechs won 4:2. In what order did they fall goals? How many game sequences were possible during the game?
• Divisible numbers
  How many 3-digit numbers can be composed of the digits 1,3,5,7,9 if the digits are not allowed to be repeated in the number notation? How many of them are divisible by five?
• Five-digit numbers
  How many different five-digit numbers can be created from the number 2,3,5 if the number 2 appears in the number twice and the number 5 also twice?
• Probability - coloured balls
  We have ten white, ten red, and ten blue balls in our pockets. We selected five white, two red, and three blue balls. What is the probability that we will pick a white ball in the next move?
• Garden centre
  A garden centre sells seedlings of not yet bloomed roses. From long-term experience it is known that 91% of these seedlings bloom red, but the remaining seedlings do not bloom at all. The average lifespan of a seedling is 36 hours. The roses are sold in b
• Playmakers + coach
  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?
• Basketball
  Peter and Frank shot baskets. Each had 20 attempts. Peter scored thirteen and Frank scored twelve. Calculate each one's success rate as a percentage.
• Committees
  How many different committees of 2 people can be formed from a class of 21 students?
• Dices
  We will throw two dice. What is the probability that the ratio between numbers on the first and second dice will be 1:2?
• Variations
  Find the number of items when the count of variations of the fourth class without repeating is 26 times larger than the count of variations of the third class without repetition.
• Password dalibor
  Camilla wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes these two changes. How many opportunities do you have a choice?

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