Permutations without repetition

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

• 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 6 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 2 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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