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

• Win in raffle
  The raffle tickets were sold to 200, 5 of which were winning. What is the probability that Peter, who bought one ticket, will win?
• MATES
  In MATES (Small Television tipping), from 35 random numbers, five winning numbers are drawn. How many possible combinations are there?
• 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?
• Roll the dice
  What is the probability that if we roll the dice, a number less than five falls?
• Brief probability
  Natalia went to the closet to pick out Daniel's briefs. Daniel has one piece of white briefs and one piece of black briefs in the closet. What is the probability that Natalie will take off his white briefs?

more math problems »