N Choose K Calculator n=100, 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

• Subsets
  How many are all subsets of set C = (97, 67, 66, 18, 59, 64)?
• Seating rules
  In a class, there are 28 seats, but in the 5.D class, there are only 24 students. How many ways can students sit? (The class has 14 benches. A bench is for a pair of students.) Result write down as powers of 10 - (logarithm - large number).
• Words
  How many 2 letters "words" are possible using 14 letters of the alphabet? a) without repetition b) with repetition
• Dice options
  We roll three dice. Write down all the feast options.
• Candy flavors
  A bag contains 20 candies in five different flavors: cherry, lemon, orange, mango, and cola. We know that there is at least one of each flavor in the pocket and that there are twice as many lemons as cherry ones. How many ways can different flavors be rep
• Digits
  How many five-digit numbers can be written from numbers 0.3,4, 5, and 7 divided by 10, and digits are repeated?
• Digit Count Numbers Sequence
  How many digits 7 are in numbers from 1 to 777?
• Probability of intersection
  Three students have a probability of 0.7,0.5, and 0.4 to graduate from university, respectively. What is the probability that at least one of them will be graduated?
• Alarm systems
  What is the probability that at least one alarm system will signal the theft of a motor vehicle when the efficiency of the first system is 90% and of the independent second system 80%?
• Probability - products
  Based on previous inspection, it is known that 3% of defective products occur during the manufacturing of a certain product. a) Calculate the probability that among 100 randomly selected products there are exactly 2 defective ones, assuming each product i
• PIN code puzzle
  My mother forgot the PIN code of her ATM card, which consisted of 4 different numbers. Help her put it together if she remembers: And - all the numbers were even B - zero in the pin code was not C - the first number was a multiple of the second number, wh
• Tournament match calculation
  The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe?
• Double six-six
  What is the probability that a player in the games of ludo will throw a double six twice?
• Hockey Championships
  At the 2021 World Hockey Championships, there are eight teams in Group A, each playing seven matches. There are 4 points for each team to gain points (3-2-1-0), but it is always paired with the opponent's points ( 0-1-2-3). How many points are there possi
• Triangle from sticks
  Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks?

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