Permutations without repetition
The calculator calculates 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.Calculation:
Vk(n)=(n−k)!n! n=10 k=4 V4(10)=(10−4)!10!=6!10!=10⋅9⋅8⋅7=5040
The number of variations: 5040
A bit of theory - the foundation of combinatorics
Permutations
The permutation is a synonymous name for a variation of the nth class of n-elements. It is thus any n-element ordered group formed of n-elements. The elements are not repeated and depend on the order of the elements in the group.P(n)=n(n−1)(n−2)...1=n!
A typical example is: We have 4 books, and in how many ways can we arrange them side by side on a shelf?
Foundation of combinatorics in word problems
- Playmakers 83340
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? - 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? - 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. - 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 - Fruits
We want to plant five fruit trees in the garden, of which three are apple trees and two pears. How many different ways can we organize them? - Syrups
In the shop, they sell three types of syrups - apple, raspberry, and orange. How many ways can you buy four bottles of syrup? - 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? - Indistinguishable 81481
How many ways can a tower of five yellow and four blue cubes be built so that each yellow cube is adjacent to at least one other yellow cube? Yellow dice are indistinguishable, and so are blue dice.
- Tic-tac-toe
In how many ways could 9 participants of the school round of five-in-a-row win the first three places? - Number 4
Kamila wrote all-natural numbers from 1 to 400 inclusive. How many times did she write the number 4? - Balls in row
Calculate the number of ways of placing four black balls, four turquoise balls, and five gold balls in a row. - You have
You have four reindeer, and you want to have 3 fly your sleigh. You always have your reindeer fly in a single-file line. How many different ways can you arrange your reindeer? - Coffe cups
We have 4 cups with four different patterns. How many possible combinations can we create from 4 cups?
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