N Choose K Calculator n=4 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

• Two doctors
  Doctor A makes the correct diagnosis with a probability of 89% and Doctor B with a probability of 75%. Calculate the probability of a correct diagnosis if both doctors examine the patient independently.
• Examination
  The class is 25 students. How many ways can we choose 5 students for examination?
• Lines
  How many points will intersect 27 different lines where no two are parallel?
• Pediatrician
  Pediatrician, this month of 20 working days takes 4 days holidays. What is the probability that it will be at work on Monday?
• Green - Red
  We have 4 bags. Each consists of one green and 2 red balls. From each, we pull just one ball. What is the probability that we don't pull any green ball?
• Hockey players
  After we cycle, five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
• Olympics
  How many ways can six athletes be placed on the podium at the Olympics? Depends on the color of the metal.
• Three digits number 2
  Find all three-digit positive integers that can be formed from the digits 1, 2, 3, and 4, subject to the following conditions: the units digit is one of 1, 3, or 4, and the hundreds digit is 4 or 2.
• Five-digit
  Find all five-digit numbers that can be formed from the digits 1, 2, 3, 4, and 5 without repetition, and then those with repeated digits. Show your calculation.
• Test - questions
  You have a test with eight questions, where you can choose from 3 answers for each question, and one answer is always correct. The probability that we answer 5 or 6 questions correctly when randomly filling in (that is, we all guess the answers) is ……. Th
• Red balls
  The bag has three red, 12 blue, and eight green balls. If we want the probability of pulling out the red balls to be 20%, how many red balls must we add to the bag?
• Pair combinations
  From 5 girls and four boys, we have to choose one pair, boy and girl. List all the pairs in which the individual boys will be. Attention, these are four examples. How many pairs are there?
• Three-digit numbers
  Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there?
• Digit Count Numbers Sequence
  How many digits 7 are in numbers from 1 to 777?
• Four-Digit Lock Codes
  How many four-digit codes on the wheel lock can we create from the digit 0,1,2,3,4,5,6,7,8,9 if it is true that we cannot repeat the numbers?

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