Permutations without repetition

The calculator computes the number of permutations of n elements. The number of permutations is the number of ways to choose a sample of n elements from a set of n distinct objects where order does matter and repetitions are not allowed. There are n! (n factorial) ways of arranging n objects into an ordered sequence.

Elements to choose from:

(n)

Calculate

A bit of theory - the foundation of combinatorics

Permutations

A permutation is an ordered arrangement of all n elements of a set, where each element is used exactly once, the order matters, and no repetition is allowed.

$P(n)=n(n-1)(n-2)...1=n!$

Example: We have 4 books. In how many ways can we arrange them side by side on a shelf?

Foundation of combinatorics in word problems

• Peak
  Uphill leads 2 paths and one lift. a) How many options back and forth are there? b) How many options to get there and back by the not same path are there? c) How many options back and forth are there that we go at least once a lift?
• Hockey players
  After we cycle, five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other?
• Dance couple arrangement
  Six boys and six girls (among them Emil, Felix, Gertrude, and Hannah) want to dance. The number of ways they can make six (mixed) couples if Emil does not want to dance with Gertrude and Hannah wants to dance with Felix is?
• Comma dot characters
  How many characters can we create from two commas and four dots?
• Book Store
  The Mabini Book Store (MBS) is reducing the prices of Mathematics books for promotion. The store has 6 Algebra books, 6 Geometry books, and 5 Statistics books to be arranged on a shelf. Books of the same kind are to be placed beside each other. How many w
• Miloš 2
  Miloš works in an optician's. He helps his friend Martin with the selection of lenses for prescription glasses. These can have: - a special anti-scratch treatment, - anti-reflection – ensures greater permeability of light into the eye, - photochromic – da
• Car parking ways
  How many ways can ten cars park side by side in a parking lot?
• Six segmants
  Given are 6 line segments with lengths of 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm. How many equilateral triangles can make from them? List all the options.
• Number pairs
  Five different positive numbers are written on the board. Determine the largest possible number of pairs formed from them in which the sum of the two elements equals one of the five numbers written on the board.
• Elements
  If the number of elements is decreased by two, the number of permutations is decreased 30 times. How many elements are?
• Digits
  How many natural numbers greater than 4000 are formed from the numbers 0,1,3,7,9 with the figures not repeated, B) How many natural numbers will be less than 4000, and can the numbers be repeated?
• Six on dice
  When throwing two dice, what is the probability they will fall at least one six?
• Three-digit numbers
  How many three-digit numbers do we make from the numbers 4,5,6,7?
• Book distribution possibilities
  There are 11 pupils in the group, among them just one Martin. How many possibilities are there for distributing 4 different books to these pupils if each is to receive at most one and Martin just one of these books".
• Couple train boarding
  Ten married couples board the train, which has five cars. How many ways can they take if no two spouses want to be in the exact vehicle?

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