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
- Seating
How many ways can 7 people sit on 5 numbered chairs (e.g., seat reservation on the train)? - Playing cards
How many possible ways are there to shuffle 6 playing cards? - 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? - Rectangles
How many rectangles with area 8855 cm² whose sides are natural numbers? - 7 heroes
6 heroes galloping on 6 horses behind. How many ways can we sort them behind?
more math problems »
