Variations without repetition

The calculator calculates the number of variations of the k-th class from n elements. Variation is a way of selecting k items from a collection of n items (k ≤ n), such that (like permutations) the order of selection does matter. The repetition of items is not allowed.

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

A bit of theory - the foundation of combinatorics

Variations

A variation of the k-th class of n elements is an ordered k-element group formed from a set of n elements. The elements are not repeated and depend on the order of the group's elements (therefore arranged).

The number of variations can be easily calculated using the combinatorial rule of product. For example, if we have the set n = 5 numbers 1,2,3,4,5, and we have to make third-class variations, their V₃ (5) = 5 * 4 * 3 = 60.

$V_k(n)=n(n-1)(n-2)...(n-k+1)=\frac{n!}{(n-k)!}$

n! we call the factorial of the number n, which is the product of the first n natural numbers. The notation with the factorial is only clearer and equivalent. For calculations, it is fully sufficient to use the procedure resulting from the combinatorial rule of product.

Foundation of combinatorics in word problems

• Flags
  How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials, so each flag consists of three different colors?
• No. of divisors
  How many different divisors have number 13 ⁴ * 2 ⁴?
• Chambers
  The decision-making committee consists of three people. For the commission's decision to be valid, at least two members must vote similarly. It is not possible not to vote in the commission. Everyone only votes yes or no. We assume that the first two memb
• Phone number
  A phone number with nine digits, none of which are repeated. The middle number in the second three-digit number is 3 times greater than the 6th and twice greater than the 7th. The three-digit number in the middle 3 numbers is 2 times greater than the last
• Alarm clock
  The old watchmaker has a unique digital alarm in its collection that rings whenever the sum of the alarm's digits equals 21. Find out when the alarm clock will ring. What is their number? List all options.

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