Considere S=\{1,2,3,4,5\}.
Liste todas as 3-permutações de S.

Passo 1

O enunciado pede para listar todas as 3-permutações de S=\{1,2,3,4,5\}. Uma 3-permuta­ção é um tuplo ordenado de tamanho 3 com elementos distintos de S. O número total é
P(5,3)=\frac{5!}{(5-3)!}=5\cdot4\cdot3=60.

Passo 2

Listamos todas as permutações cujo primeiro elemento é 1: (1,2,3), (1,2,4), (1,2,5), (1,3,2), (1,3,4), (1,3,5), (1,4,2), (1,4,3), (1,4,5), (1,5,2), (1,5,3), (1,5,4).

Passo 3

Listamos todas as permutações cujo primeiro elemento é 2: (2,1,3), (2,1,4), (2,1,5), (2,3,1), (2,3,4), (2,3,5), (2,4,1), (2,4,3), (2,4,5), (2,5,1), (2,5,3), (2,5,4).

Passo 4

Listamos todas as permutações cujo primeiro elemento é 3: (3,1,2), (3,1,4), (3,1,5), (3,2,1), (3,2,4), (3,2,5), (3,4,1), (3,4,2), (3,4,5), (3,5,1), (3,5,2), (3,5,4).

Passo 5

Listamos todas as permutações cujo primeiro elemento é 4: (4,1,2), (4,1,3), (4,1,5), (4,2,1), (4,2,3), (4,2,5), (4,3,1), (4,3,2), (4,3,5), (4,5,1), (4,5,2), (4,5,3).

Passo 6

Listamos todas as permutações cujo primeiro elemento é 5: (5,1,2), (5,1,3), (5,1,4), (5,2,1), (5,2,3), (5,2,4), (5,3,1), (5,3,2), (5,3,4), (5,4,1), (5,4,2), (5,4,3).

Resposta

(1,2,3), (1,2,4), (1,2,5), (1,3,2), (1,3,4), (1,3,5), (1,4,2), (1,4,3), (1,4,5), (1,5,2), (1,5,3), (1,5,4) (2,1,3), (2,1,4), (2,1,5), (2,3,1), (2,3,4), (2,3,5), (2,4,1), (2,4,3), (2,4,5), (2,5,1), (2,5,3), (2,5,4) (3,1,2), (3,1,4), (3,1,5), (3,2,1), (3,2,4), (3,2,5), (3,4,1), (3,4,2), (3,4,5), (3,5,1), (3,5,2), (3,5,4) (4,1,2), (4,1,3), (4,1,5), (4,2,1), (4,2,3), (4,2,5), (4,3,1), (4,3,2), (4,3,5), (4,5,1), (4,5,2), (4,5,3) (5,1,2), (5,1,3), (5,1,4), (5,2,1), (5,2,3), (5,2,4), (5,3,1), (5,3,2), (5,3,4), (5,4,1), (5,4,2), (5,4,3)

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