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Symmetric Set Degree n

If

Obviously, a set of three elements will have

Let

Let

Since

………….

………….

Hence in all

**S**is a finite set containing**n**distinct elements, then there will be**n!**distinct arrangements of the elements of set**S**. The set of all these**n!**arrangements is denoted by**S**_{n}and is known as symmetric set of permutations of degree**n**or symmetric set of degree**n**. Also**Sn = {ƒ : ƒ**is a permutation of degree**n}**Obviously, a set of three elements will have

**3!**Elements, i.e.**S**_{3}will have been**3!**or**6**elements.Let

**S = {1, 2, 3, …., n}.**Let

**ƒ S**_{n}be a permutation of**S**_{n}. This can be exhibited asSince

**ƒ**is one-one onto, so we have**n**choices for**(1)ƒ**

**(n – 1)**choices for**(2)ƒ**………….

………….

**1**choice for**(n)ƒ**Hence in all

**n(n – 1) (n – 2) …… 3.2.1. = n!**functions**ƒ S**_{n}can arise. Thus**S**_{n}has**n!**elements.**Services: -**Symmetric Set Degree n Homework | Symmetric Set Degree n Homework Help | Symmetric Set Degree n Homework Help Services | Live Symmetric Set Degree n Homework Help | Symmetric Set Degree n Homework Tutors | Online Symmetric Set Degree n Homework Help | Symmetric Set Degree n Tutors | Online Symmetric Set Degree n Tutors | Symmetric Set Degree n Homework Services | Symmetric Set Degree nSubmit Your Query ???

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