Question

Find the number of even and odd permutations in sn for all n

Answer 1

Answer:

For n ≥ 2, the permutations in the symmetric group Sₙ are divided half and half between even and odd permutations.  Thus:

• the number of even permutations is n! / 2
• the number of odd permutations is n! / 2

For n = 1, the group S₁ is trivial.  The only permutation is the identity, which is even.  Thus:

• the number of even permutations is 1
• the number of odd permutatioins is 0