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
- Phone numbers
How many 9-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated? - 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) - 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? - 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? - Subsets
How many are all subsets of set C = (97, 67, 66, 18, 59, 64)? - 7 heroes
6 heroes galloping on 6 horses behind. How many ways can we sort them behind? - Toys
3 children pulled 12 different toys from a box. How many ways can toys be divided so each child has at least one toy? - Pairs
At the table sit 10 people, 5 on one side and 5 on the other side. Among them are 3 pairs. Every pair wants to sit opposite each other. How many ways can they sit? - Vans
In how many ways can 5 shuttle vans line up at the airport? - Digits
Write the smallest and largest 2-digit natural number.
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