N Choose K Calculator

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n choose k calculatorFind 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

Calculation:

Ck(n)=(kn)=k!(n−k)!n! n=10 k=4 C4(10)=(410)=4!(10−4)!10!=4⋅3⋅2⋅110⋅9⋅8⋅7=210

The number of combinations: 210

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: Ck(n)=(kn)=k!(n−k)!n! 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

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%.
Dice How many times must you throw the dice, and was the probability of throwing at least one pětky greater than 70%?
Seating How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
Playing cards How many possible ways are there to shuffle 6 playing cards?
Chess How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
Two doctors Doctor A will determine the correct diagnosis with a probability of 89% and doctor B with a probability of 75%. Calculate the probability of proper diagnosis if both doctors diagnose the patient.
Area codes How many 4 digit area codes are possible if the first number can't be zero?
2nd class variations From how many elements can you create 5112 variations of the second class?
Chords How many 5-tónových chords (chord = at the same time sounding different tones) is possible to play within 10 tones?
Guests How many ways can 8 guests sit down on 10 seats standing in a row?
Examination The class is 25 students. How many ways can we choose 5 students for examination?
Bits, bytes Calculate how many different numbers can be encoded in a 64-bit binary word.
Subsets How many 19 element subsets can be made from the 26 element set?
Event probability The probability of event N in 5 independent experiments is 0.4. What is the probability that the event N occurs in one experiment (chance is the same)?
Rectangles How many rectangles with area 8855 cm² whose sides are natural numbers?