n choose k calculator n=3, k=1 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

• Lottery
  The lottery is 60000 elk, in which 6200 wins. What is the probability that the purchase of 12 elks won nothing?
• Morse alphabet
  Calculate how many words of Morse code to create compiling dashes and dots in the words of one to piatich characters.
• Shooter
  The probability that a good shooter hits the center of the target circle No. I is 0.1. The probability that the target hit the inner circle II is 0.58. What is the probability that it hits the target circle I or II?
• Calculation of CN
  Calculate: (486 choose 159) - (486 choose 327)
• Cars plates
  How many different license plates can a country have since they use 3 letters followed by 3 digits?

more math problems »