Variations

Take a set S of m different elements. Choose n elements in a specific order. Each such choice is called a variation of m elements choose n. Two variations are different if they have different elements or if they are in a different order. The number of these variations is:

Vm,n= m· (m-1)· (m-2)·……(m- n +1)

Example : From a class of 20 students you choose 3 students in a particular order. Such a choice is a variation of 20 elements choose 3.
V20,3= 20· 19· 18 = 6840

 

Take a set S of m different elements. Choose n elements in a specific order and, now, it is permitted to indicate the same element several times. Each such choice is called a variation with repetition of m elements choose n.  Two variations are different if they have different elements or if they are in a different order. The number of these variations is:
VRm,n= mn

Example : How many codes of 4 letters can you get with a, b and c?  These are variations with repetition of 3 elements choose 4:   VR3,4= 34 = 81    

 

Exercise:

a) How many different even numbers composed of 4 digits can you make with the digits 1, 2, 3, 4, 5 and 6?

b) And if all digits were different?

 

 

 

 

 

Solutions: a) 375; b) 180

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