Variations with repetition

The calculator calculates 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 of the k-th class of n elements is an ordered k-element group formed of a set of n elements, wherein the elements can be repeated and depends on their order. A typical example is the formation of numbers from the numbers 2,3,4,5, and finding their number. We calculate their number according to the combinatorial rule of the product:

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

Foundation of combinatorics in word problems

• Variations 3rd class
  From how many elements can we create 13,800 variations of the 3rd class without repeating?
• Four swords
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• Tournament
  Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other?
• Seven
  Seven friends agreed to send everyone a holiday card. How many postcards were sent?
• Three-part novel
  In how many ways can seven books be stored on a shelf if there is one three-part novel to be placed side by side?
• Bookshelf and books
  How many ways can we place seven books on a bookshelf?
• Gradually 67284
  Petra borrowed four books from the library at the beginning of the summer holidays. How many orders in which she could gradually read them?

• Constructed 67424
  There are six lines 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm long, two of each length. How many isosceles triangles can be constructed from them? List all options.
• Three-digit 72184
  How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?
• Probability 72324
  When entering the PIN code, we used the digits 2, 3, 4, 5, and 7 only once. What is the probability that someone will guess our PIN code on the first try?
• Prize
  How many ways can 9 participants be rewarded with the first, second, and third prizes in a sports competition?
• Sum on dice
  We have two dice. What is the greater likelihood of falling a total sum of 7 or 8? (write 7, 8, or 0 if the probabilities are the same)?
• Inverted nine
  In the hotel Inverted Nine, each hotel room number is divisible by 6. How many rooms can we count with the three-digit number registered by digits 1, 8, 7, 4,9?
• Four-digit 7953
  How many four-digit codes on the wheel lock can we create from the digit 0,1,2,3,4,5,6,7,8,9 if it is true that we cannot repeat the numbers?
• Possible combinations - word
  How many ways can the letters F, A, I, and R be arranged?

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