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

• Two doctors
  Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.
• Examination
  The class is 25 students. How many ways can we choose 5 students for examination?
• Lines
  How many points will intersect 27 different lines where no two are parallel?
• Pediatrician
  Pediatrician, this month of 20 working days takes 4 days holidays. What is the probability that it will be at work on Monday?

• Green - Red
  We have 5 bags. Each consists of one green and 2 red balls. From each, we pull just one ball. What is the probability that we don't pull any green ball?

more math problems »