Permutations without repetition n=7 result

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

• 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 Lock Codes
  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?
• Combinatorial examples
  1. In the class you have 15 pupils. In how many ways can we select four for examination? 2. In how many ways can we select from seven-card cards (32 cards) any two cards? 3. In how many ways can we divide 12 pupils into two six-member teams? 4. In how man
• Numbered
  In the past, passengers on public transport validated single-use tickets that had 9 numbered boxes, a certain number of which were punched with a validator. A) In how many different ways could a ticket be validated if 3 boxes were punched? B) In how many
• Six-digit number creation
  How many 6-digit numbers can be created from the number 1,2,3,4,5,6 if we must not repeat the numbers?
• 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?
• 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?
• Farewell photos
  At the end of the school year, ninth-grade boys and girls said goodbye by exchanging photos with each other. A total of 552 photos were exchanged. How many students were there?
• Bench seating arrangements
  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 arranged on a shelf if the three volumes of a novel must always be placed side by side?
• Prize award ways
  How many ways can the first, second, and third prizes be awarded to the 15 participants in the math competition?

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