Permutations without repetition n=4 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
  How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)?
• Rectangles
  How many rectangles with an area of 8855 cm² have sides that are natural numbers?
• Toys
  3 children pulled 6 different toys from a box. How many ways can toys be divided so each child has at least one toy?
• 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?
• Three digits number
  From the numbers 1, 2, 3, 4, and 5, create three-digit numbers whose digits do not repeat, and the number is divisible by 2. How many numbers are there?
• 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?
• Permutations
  How many 4-digit numbers can be composed of numbers 1,2,3,4,5,6,7 if: a, the digits must not be repeated in the number b, the number should be divisible by five, and the numbers must not be repeated c, digits can be repeated
• Four-digit numbers
  Create all four-digit numbers from digits 1,2,3,4,5, which can repeat. How many are there?
• Goal divisions
  School players scored seven goals in the match. List all possible goal divisions into three-thirds and add up how many.
• 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
• Three-digit code
  The five cards with the numbers 1, 2, 3, 4, and 5 put together all three-digit odd numbers. How many are there?
• 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?
• Page numbering
  The book has 88 pages. How many times is the number 4 used for the book numbering?
• Six on dice
  When throwing two dice, what is the probability they will fall at least one six?

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