Why do I get an UnsupportedOperationException when trying to remove an element from a List?

Quite a few problems with your code:

On Arrays.asList returning a fixed-size list

From the API:

Arrays.asList: Returns a fixed-size list backed by the specified array.

You can't add to it; you can't remove from it. You can't structurally modify the List.

Fix

Create a LinkedList, which supports faster remove.

List<String> list = new LinkedList<String>(Arrays.asList(split));

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On split taking regex

From the API:

String.split(String regex): Splits this string around matches of the given regular expression.

| is a regex metacharacter; if you want to split on a literal |, you must escape it to \|, which as a Java string literal is "\\|".

Fix:

template.split("\\|")

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On better algorithm

Instead of calling remove one at a time with random indices, it's better to generate enough random numbers in the range, and then traversing the List once with a listIterator(), calling remove() at appropriate indices. There are questions on stackoverflow on how to generate random but distinct numbers in a given range.

With this, your algorithm would be O(N).

This one has burned me many times. Arrays.asList creates an unmodifiable list. From the Javadoc: Returns a fixed-size list backed by the specified array.

Create a new list with the same content:

newList.addAll(Arrays.asList(newArray));

This will create a little extra garbage, but you will be able to mutate it.

Probably because you're working with unmodifiable wrapper.

Change this line:

List<String> list = Arrays.asList(split);

to this line:

List<String> list = new LinkedList<>(Arrays.asList(split));