Permutations without repetition n=10 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

• Competition
  Fifteen boys and ten girls are in the class. In the school competition, a six-member team composed of four boys and two girls is selected. How many ways can we choose students?
• Four swords
  Obelix has three helmets, four swords, and five shields. How many words must you make at the blacksmith forge Metallurgix to be able to walk another 90 days in unique armor?
• Tournament
  Six teams entered the basketball tournament. How many matches will be played if each team has to play one match with the other?
• 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?
• Triangle from sticks
  Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks?
• Book reading orders
  Patricia borrowed four books from the library at the beginning of the summer holidays. How many orders in which she could gradually read them?
• Isosceles triangle construction
  There are six lines 3 cm, 4 cm, 5 cm, 7 cm, 8 cm, and 9 cm long, two of each length. How many isosceles triangles can be constructed from them? List all options.
• Three-digit number creation
  How many three-digit numbers can be created from the numbers 1, 2, 3, and 4 if you can repeat them?
• PIN code probability
  When entering the PIN code, we used the digits 2, 3, 4, 5, and 7 only once. What is the probability that someone will guess our PIN code on the first try?
• Socks
  Ben's favorite colors are blue and green. He has six blue socks and six green socks in his sock drawer. Unfortunately, they are completely mixed up, and one day, he has to grab some socks to wear in complete darkness. How many socks (minimum) does he have
• Permutation element count
  From how many elements can we make 5040 permutations without repetition?
• Diagonals
  What is the number of diagonals of a decagon?
• Flower - permutations
  At a flower shop, there are 5 different kinds of flowers: tulips, lilies, daisies, carnations, and roses. There are also 3 different colours of vases: blue, green, and pink. If one kind of flower and one colour of vase are selected at random, what is the
• Permutations without repetition
  From how many elements can we create 720 permutations without repetition?
• Elements
  If the number of elements is decreased by two, the number of permutations is decreased 30 times. How many elements are?

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