I have two groups with n balls marked from 1 to n.

Two groups are randomized ( i.e. for each ball in each group to get any place in new order from 1 to n the probability is 1/n )

What the probability that in new order I won't see right combinations (1-1 or 2-2 , or 3-3 , or 4-4 ...)

Simple example :

Initial order

Group 1 Group 2

1 3

2 2

3 1

Final order

1 1

2 3

3 2

Final order isn't good I don't want to see (1-1) .