maths
posted by Anonymous .
6 people are playing Secret Santa for Christmas. They will each give one gift to someone, and each receive one gift from someone. They are not allowed to give their gift to themselves. How many different ways are there to do so?

BRILLIANT SCHOLARS ROCKS !

Let's think of the question this way:
Suppose you sit the 6 people around a round table.
Then everybody gives a present to the person on their left.
So everybody has given a present and received a present.
If we change the "arrangement" of the 6 people around the table, we have a different Secret Santa arrangement.
So all we have to do is calculate the number of ways we can sit 6 people around a round table, (or let them form a circle)
that would be 6!/6 = 5! = 120
(I divided by 6. Here is why. If everybody got up and moved one to the right, the order would not change, and we can do that 6 times) 
no, its wrong