Permutations

Take a set S of n different elements. Choose the n elements in a specific order. Each such choice is called a permutation of the n elements. Two permutations are different if the elements are in a different order. The number of these permutations is:

Pn= Vn,n= n· (n-1)· (n-2)·……1 = n! (n factorial)

Example 1: Arrange 4 different marbles in one row. There are P4 = 4! = 24 different possibilities.

Example 2:

•The batmobile has 5 chairs.
•There are 5 people who need a lift.
•How many seating options are there?
 
 
Take a set S of n different elements where the first element repeats n1 times, the second element repeats n2, ….. the kth element repeats nk times ( n1 + n2 + …… nk = n). Choose these elements in a specific order. Each such choice is called a permutation with repetition of the n elements.  Two permutations are different if the elements are in a different order. The number of these permutations is:
 

Example: How many different numbers composed of 10 digits can we do with 5 ones, 2 twos, 2 threes and 1 four?
 
 
 
 
 
Exercises:
 
1) How many different unique combinations of letters can be created by rearranging the letters in the word "mathematics"?
 
2) We have 5 cats and 5 mice of different sizes. How many different pairs of one cat running after one mouse can we get? And if the smallest cat always went after the smallest mouse?
 
 
 
 
 
 
 
 
 
 
 
 
Solutions: 1) 4.989.600 2) 120; 24
 

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