Permutations without repetition n=3 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

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