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

• 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)
• Flags
  How many different flags can be made from green, white, blue, red, orange, yellow, and purple materials if each flag consists of three stripes of different colours?
• 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?
• Peak
  Uphill leads 2 paths and one lift. a) How many options back and forth are there? b) How many options to get there and back by the not same path are there? c) How many options back and forth are there that we go at least once a lift?
• Logik game
  Letter game Logik is a two-player game that has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers. The first number
• 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-digit numbers
  How many three-digit numbers are from the numbers 0, 2, 4, 6 8 (with/without repetition)?
• 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.
• Four-digit numbers
  Create all four-digit numbers from digits 1,2,3,4,5, which can repeat. How many are there?
• Dice probability
  Jana rolls two dice at the same time. What is the probability that she will score a total of four points?
• Choosing Colors for Sweater
  Danka knits a sweater and has a choice of seven colors. a) How many ways can he choose three colors for the sleeves? b) He wants ribbons of four colors on his back. How many options does he have to choose from?
• Boys and girls
  There are eight boys and nine girls in the class. There were six children on the trip from this class. What is the probability that: a) only boys went on the field trip b) just 2 boys went on the field trip
• Three-digit number
  Find all three-digit numbers n with three different non-zero digits divisible by the sum of all three two-digit numbers we get when we delete one digit in the original number.
• 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

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