n choose k calculator n=13983816, k=50 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

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• Cards
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• Chambers
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• Three digits number 2
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• Eight blocks
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• Cards
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• Divisible by five
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• Tricolors
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• Three-digit 5226
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• Dice
  We threw ten times playing dice. What is the probability that the six will fall exactly four times?
• Utopia Island
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• Two-digit 7410
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• Different 9711
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