Permutations without repetition n=7 result

The calculator computes the number of permutations of n elements. 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 repetition 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

• 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?
• 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?
• 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
• 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?
• Different Report Cards
  There are 19 children in class 6A, 7 subjects, and no one has a worse grade than a three. Can each of them have a different certificate? How many would have to be in the class so that everyone could not have another report card?
• A basket 4
  A basket contains 9 fruits, where 4 are oranges, and the rest are mangoes. Three fruits are taken out one at a time and put aside. Find the probability that 3 are oranges.
• Playmakers + coach
  In a basketball game, two pivots, two wings, and one point guard play. The coach has three pivots, four wing players, and two playmakers available on the bench. How many different five players can a coach send to the board during a game?
• Chess
  How many ways can you select 4 fields on a classic chessboard with 64 fields so that fields don't have the same color?
• Keyboards keys
  Michael had small keys on the shelf, which you can see in the picture. Their tones were marked on the white keys. Little Clara found the keys. As she took them off the shelf, they fell out of her hand, and all the white keys spilled out. So that the broth
• Elements
  If the number of elements is decreased by two, the number of permutations is decreased 30 times. How many elements are?
• Three numbers
  We have three different non-zero digits. We will create all three-digit numbers from them and use all three figures in each. We add all the made numbers and get the sum of 1554. What were the numbers?
• STRESSED word
  Each letter in STRESSED is printed on identical cards, one letter per card, and assembled in random order. Calculate the probability that the cards spell DESSERTS when assembled.
• Twelve-position number system
  Write the 12 largest five-digit numbers in the twelve-position system and the 12 smallest six-digit numbers.
• Probability
  A man had 4 coins, some $2, some $1. The coins had a number on one side and a picture on the other. The man flipped them, and the sum of the numbers on the tops of the coins was 1. The probability of this happening was 1/8. What was the probability that i
• Team selection ways
  Seven people need to be selected from the sports club, where 11 men and nine women. How many ways can we do this if seven women are on the team?

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