Variations with repetition

The calculator computes the number of variations with repetition. A variation of the k-th class with repetition of n elements is any ordered k-element group composed of only these n elements such that each element can be repeated any number of times.

Elements to choose from:

(n)

Elements chosen:

(k)

Calculate

A bit of theory - the foundation of combinatorics

Variations with repetition

A variation with repetition of the k-th class of n elements is an ordered k-element group formed from a set of n elements, where elements can be repeated and order matters. A typical example is forming numbers from the digits 2, 3, 4, 5 and counting how many such numbers exist. We calculate the count using the combinatorial rule of product:

$V_k^{\prime }(n)=n\cdot n\cdot n\cdot n...n=n^k$

Foundation of combinatorics in word problems

• N-gon
  How many diagonals does a convex 30-gon have?
• Seating
  How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
• School trip
  The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number)
• Flags
  How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials if each flag consists of three stripes of different colours?
• Rectangles
  How many rectangles with an area of 8855 cm² have sides that are natural numbers?

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