Randomly assign the best position, efficient algorithm

Pi, Board, School, District, Diameter
Assumption: Now there are 100 candidates whose numbers are 1-100
The examination room is now 10 * 10 (10 people per row)
Now it is required that the seat number is randomly assigned, not fixed from row 1 to 100

I have already figured it out, but the efficiency is relatively low, and the above is just an example, is there any other good method, please ask!

1. Fill 1->100 into the linked list data structure R such as arraylist
2. Let N=100,
3. Take new Random().Next(1, N) to get the result n
4. Remove the element r at position n in R, the element r is the assigned position,
5. In the matrix corresponding to r to 10*10, get the assigned position
7. Repeat step 2 until N=0, that is, all positions are allocated

. Take new Random().Next(1, N) to get the result n
Is there a high probability that the result n obtained in this step will appear the same?
Very high,
For example, if you get 1 for the first time, the first element of the arraylist will be removed, which is 1, and the seat number is 1, 1.
The second time it gets 1 again, the first element of the arraylist is removed, namely 2, the seat number is 2, 1