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 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: Ck(n)=(kn)=k!(n−k)!n! 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

Examination The class is 25 students. How many ways can we choose 5 students for examination?
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?
No. of divisors How many different divisors have number 13 4 * 2 4?
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):
Ace We pulled out one card from a complete set of playing cards (32 cards). What is the probability of pulling the ace?