Permutations without repetition

The calculator calculates the number of permutations of n elements. 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 repetition 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

The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.

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

A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?

Foundation of combinatorics in word problems

• 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?
• Olympics
  How many ways can six athletes be placed on the podium at the Olympics? Depends on the color of the metal.
• Three-digit numbers
  Use the number 4,5,8,9 to write all three-digit numbers without repetition. How many such numbers are there?
• 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?
• Numbered
  In the past, passengers in public transport vehicles marked such single-use tickets, which had 9 numbered boxes, a certain number of which were punched with a marker. A) In how many different ways could the ticket be marked if 3 boxes were punched? B) How
• Gertrude 62304
  Six boys and six girls (among them Emil, Félix, Gertrude, and Hanka) want to dance. The number of ways they can make six (mixed) couples if Emil does not want to dance with Gertrude and Hanka wants to dance with Felix is?
• 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

• Three-digit numbers
  How many three-digit numbers are from the numbers 0, 2, 4, 6 8 (with/without repetition)?
• Elements
  If the number of elements is decreased by two, the number of permutations is decreased 30 times. How many elements are?
• Ninth-grade 5446
  When the ninth-grade boys and girls said goodbye at the end of the school year, they each gave each other their photos. It was a total of 552 images. How many farewells were there?
• Friends 7624
  Five friends want to sit on one bench. How many ways can this be done if one of them always sits in the middle of the bench?
• 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?
• Participants 31351
  How many ways can the first, second, and third prizes be awarded to the 15 participants in the math competition?
• According 63394
  Three boys and four girls. How many ways can they be placed side by side according to gender?
• Other
  On other days, I often see two colors in front of my eyes - blue and yellow. I feel sad about what is happening. That is why I have a role for you today about colors. I have 5 markers in my pencil case: blue, yellow, green, red, and purple. How many ways

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