n choose k calculator

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.

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

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:

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

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

• Olympics metals
  How many ways can one win six athletes' medal positions in the Olympics? Metal color matters.
• Five-digit
  Find all five-digit numbers that can be created from number 12345 so that the numbers are not repeated and then numbers with repeated digits. Give the calculation.
• Determined 3570
  There are 12 points in space, with no three lying on a straight line. How many different planes are determined by these points?
• A fair 2
  A fair die is thrown two times. What is the probability that the sum of the score is almost 8?
• Ten dices
  When you hit ten dice simultaneously, you get an average of 35. How much do you hit if every time you get six, you're throwing the dice again?
• Three shooters
  Three shooters shoot, each time, on the same target. The first hit the target with 0.7, the second with 0.8, and the third with 0.9 probability. What is the probability of hitting the target: a) just once b) at least once c) at least twice
• 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 3 digits?
• 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?
• Olympics
  How many ways can six athletes be placed on the podium at the Olympics? Depend on the color of the metal.
• Hockey game
  In the hockey game, they made six goals. The Czech played against Finland. The Czechs won 4:2. In what order to fall goals? How many game sequences were possible during the game?
• Hockey match
  The hockey match ended with a result of 3:1. How many different storylines may the match have?
• Event probability
  The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (chance is the same)?
• 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?
• 7 heroes
  6 heroes galloping on 6 horses behind. How many ways can we sort them behind?
• VCP equation
  Solve the following equation with variations, combinations, and permutations: 4 V(2,x)-3 C(2,x+ 1) - x P(2) = 0

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