Discrete Math Permutations help

Question

Is it true that there are $5!$ possible sequences of five specific names? Wouldn't this be true since there are $5!$ arrangements?

Answer 1

Yes, these are the permutations on $5$ elements. There are $5!=120$ permutations, and they are listed below.

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