Calculating individual orders in this Probability question

Calculating individual orders in this Probability question

I have a probability question to solve:
Question: Three different orders are to be mailed to three suppliers.
However, an absent minded secretary gets the orders mixed up and sends
them randomly. If a match refers to the fact that a suppliers receives the
correct order, find the probability of the event that no matches occur.
Solution given:
P(no matches) = 1 - P(at least one match)
P(at least one match) = P(first match)+ P(second match) + P(third match) -
P(first match and second match) - P(first match and third match) -
P(second match and third match) + P(first match and second match and
third match)
P(at least one match) = (2!/3! * 3) -(1!/3! *3) +(1!/3!)
P(no match) = 1 - P(at least one match)
My question is why the Probability for each match is 2!/3!. Not sure how
to get it. Need some guidance