N Choose K calculator n=100, k=10 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

• Probability - tickets
  What is the probability when you have 25 tickets in 5000 that you do not win the first (one) prize?
• Family
  What is the probability that a family with 3 children has: exactly 1 girl? 2 girls and 1 boys? Consider the birth probability of a girl as 48.66% and a boy as 51.34%.
• Phone numbers
  How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?
• Dice
  How many times must you throw the dice, and was the probability of throwing at least one pětky greater than 70%?
• Lottery
  The lottery is 47000 elk, in which 4800 wins. What is the probability that the purchase of 6 elks won nothing?

more math problems »