Five teachers at a meeting remove their name tags and put them in a bag. One by one, each teacher randomly draws one tag from the bag until the bag is empty. What is the probability that exactly one of the teachers draws the correct name tag?

i got this so far...

one person gets their name and four of the people dont get their names: P(that)= 1/5 * 3/4 * 2/3 * 1/2 * 1 = .05

then since the order may happen any given way, we multiply by the number of arrangements possible: 5 "5 choose 1 = 5!/[4!1!]"

ans = .25

answer looks wrong