n choose k calculator n=7, k=2 result

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

• Rectangles
  How many rectangles with area 8855 cm² whose sides 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 6615
  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 8280
  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?
• 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 Franta threw to the basket. Each had 20 attempts. Peter scored thirteen and twelve Franta. Give them a percentage of success.
• 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
  Kamila 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?
• Probability 2386
  We throw a die seven times. What is the probability that: a) the first, second, and third times fall six and not in all the others, b) 5 does not fall four times in a row, and yes, in the last 3 hours?

more math problems »