N Choose K Calculator n=111, k=10 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

• Dice
  How many times must you throw the dice, and was the probability of throwing at least one pětky greater than 70%?
• Subsets
  How many 19 element subsets can be made from the 26 element set?
• Rectangles
  How many rectangles with an area of 8855 cm² have sides that are natural numbers?
• Calculation of CN
  Calculate: (486 choose 159) - (486 choose 327)
• Toys
  3 children pulled 6 different toys from a box. How many ways can toys be divided so each child has at least one toy?
• Probabilities
  If probabilities of A, B, and A ∩ B are P (A) = 0.62, P (B) = 0.78, and P (A ∩ B) = 0.26, calculate the following probability (of the union. intersect and opposite and its combinations):
• Words
  How many 2 letters "words" are possible using 14 letters of the alphabet? a) without repetition b) with repetition
• Ace
  We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace?
• Three digits number
  From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there?
• Intersection of the lines
  How many points do nine lines intersect in a plane, of which four are parallel, and of the other five, no two are parallel (and if we assume that only two lines pass through each intersection)?
• Cards
  The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace
• Two-digit numbers
  Write all the two-digit numbers that can be composed of the digit 7,8,9 without repeating the digits. Which ones are divisible b) two, c) three d) six?
• Three-digit code
  The five cards with the numbers 1, 2, 3, 4, and 5 put together all three-digit odd numbers. How many are there?
• Probability - triangles
  We have five lines with lengths of 3 cm, 5 cm, 7 cm, 9 cm, and 11 cm. What is the probability that we will be able to construct a triangle with randomly selected three?
• First class
  The shipment contains 40 items. 36 are first-grade, and four are defective. How many ways can we select five items so that it is no more than one defective?

more math problems »