Permutations without repetition n=11 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

• School trip
  The class has 19 students. How can students be accommodated in the hostel, where available 3× 2-bed, 3× 3-bed and 1× 4-bed rooms? (Each room has its unique number)
• 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?
• Dices throws
  What is the probability that the two throws of the dice: a) Six falls even once b) Six will fall at least once
• Metals
  Eight teams play in the Hockey World Cup. Determine how many ways gold, silver, and bronze medals can be awarded.
• Darts Score Combinations
  Adam was practicing for a darts competition in class. Every day at home, he threw darts at a target in which the individual fields were worth 1,3 and 5 points. He threw 9 darts every day and always scored 27 points. He is in good form and never missed a t
• A pizza
  A pizza place offers 14 different toppings. How many different three-topping pizzas can you order?
• 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?
• Five-digit number repetition
  How many five-digit numbers can we make from digits 2,3,4,6,7,9 if they can repeat with the digits?
• Cookie selection ways
  It was Tibor's birthday, and he bought 8 different cookies for his friends (Horalky, Tatanky, Kávenky, Attack, Mila, Anita, Mäta, Lina). He put them all in a box, and each friend could choose two pieces. Tanya chose first. Which two cookies could Táňa cho
• 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.
• Volleyball tournament teams
  The school volleyball tournament was played on a one-on-one basis. One match lasted 15 minutes, and 3 hours and 45 minutes were played. Calculate how many teams participated.
• Triangles - combinations
  How many different triangles with sides of whole centimetres have a perimeter of 12 cm?
• Salami
  We have six kinds of salami, six of which have ten pieces, and one of which has four pieces. How many ways can we distinctly choose five pieces of salami?
• Raffle
  There are 200 tickets in a raffle, but only 20 are winners. What is the probability that a group of people who bought 5 tickets together wins at least 4 prizes?
• PIN code
  The PIN on Michael's credit card is a four-digit number. Michael told his friend: • It is a prime number - a number greater than 1, which is only divisible by the number one and by itself. • The first digit is larger than the second. • The second digit is

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