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
- N-gon
How many diagonals have convex 30-gon? - Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - 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, so each flag consists of three different colors? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - Word
What is the probability that a random word composed of chars S, G, R, S, E, I, N, A, L, P, C, T, M, H, E, E will be the SPHERICALSEGMENT? - 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? - Vans
In how many ways can 5 shuttle vans line up at the airport? - Kids
How many different ways can sit 6 boys and 3 girls in line if girls want to sit on the edge? - Shelf
How many ways are there to arrange 6 books on a shelf? - 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? - Locker Code Possibilities
Peter forgot the four-digit code to his school locker lock. Fortunately, his mother remembered some information about him. He knows that the first binary number is divisible by 15 and the second by 7. However, Peter is a big loser, so he has to try all th - 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 - Password
The voltage station is day changing the master password, which consists of three letters. The code generation process does not change and is based on the following procedure: The following letters (A) to (I) correspond to different numbers from 1 to 9 if - 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?
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