Permutations without repetition n=42 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

• Seating
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• Rectangles
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• Hockey players
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• Olympics
  How many ways can six athletes be placed on the podium at the Olympics? Depends on the color of the metal.
• Hockey match
  The hockey match ended with a result of 3:1. How many different storylines may the match have?
• Security
  The safe's security code is set with three dials. The first dial has five different letters, the second dial has the numbers 0 to 4, and the third dial has the numbers 5 to 9. One code can be set in approximately 1 second. How should the alarm be timed so
• Permutations Equation Elements
  Seven times the permutations of n elements equal one-eighth of the permutations of n + 2 elements. What is the number of elements?
• Three-digit numbers
  How many three-digit numbers do we make from the numbers 4,5,6,7?
• Four 12
  Four classmates (Ivan, Matej, Fero, Ľuboš), who go to school by the same tram connection, agreed that they would meet in the morning at the stop in front of the school. As they promised, so it happened. The first classmate arrived at the stop in front of
• Refrigerator, lemonades
  How many possible ways can we store three lemonades, four mineral waters, and two juices in the refrigerator next to each other?
• Playmakers + coach
  In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game?
• Password dalibor
  Camilla wants to change the password daliborZ by a) two consonants exchanged between themselves, b) changes one little vowel to such same great vowel c) makes these two changes. How many opportunities do you have a choice?
• Group combinations
  The group has 12 red girls and 25 blue girls in costumes. How many of them can we put together a group of 6 girls so that the four girls have red outfits?
• Elements
  If the number of elements is decreased by two, the number of permutations is decreased 30 times. How many elements are?
• How many
  How many double-digit numbers greater than 30 can we create from digits 0, 1, 2, 3, 4, and 5? We cannot repeat numbers in a two-digit number.

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