n choose k calculator n=112, k=3 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

• Calculation of CN
  Calculate: (486 choose 159) - (486 choose 327)
• Cards
  The player gets eight cards of 32. What is the probability that it gets a) all four aces b) at least one ace
• Student examination
  How many ways can a teacher select a group of 6 students to sit in the front row if the class has 13 students?
• Menu choice
  In a Jollibee, you have a menu choice of C1, C2, and C3. For dessert, you have a choice of ice cream and mango peach. How many different options do you have?
• Four-digit 79614
  Determine the number of all four-digit natural numbers in decimal notation in which the digit 0 is not present, and each of the remaining nine numbers occurs at most once.
• Contestants 67104
  The contestants have to create an ice cream sundae containing three different types of ice cream. They can use cocoa, yogurt, vanilla, hazelnut, punch, lemon and blueberry ice cream. How many different ice cream sundaes can the contestants create?
• 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):
• Probability 80856
  The probability of occurrence of a certain phenomenon is the same in all trials and is equal to 0.7. Attempts are repeated until this phenomenon occurs. What is the probability that we will have to make a fifth trial?
• 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?
• 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)?
• Probability 71784
  What is the probability that if you roll the die twice, the sum of 12 will fall?
• Dice
  We threw ten times playing dice. What is the probability that the six will fall exactly four times?
• Probability 69714
  The factory produces 35% of the tiles on line A, which produces scrap with a probability of 0.02, and 65% on line B, where the probability of scrap is 0.03. What is the probability that the selected tile will be defective?
• Six on dice
  When throwing two dice, what is the probability they will fall at least one six?
• Four-digit 65124
  Please find out how many different four-digit numbers we can create from the digits 3 and 8 so that the two digits three and two digits eight are used in each four-digit number created.

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