at random – English Grammar Profiler
In the English Vocabulary Profile, the adverbial phrase ‘at random’ is listed at C1 with the meaning:
chosen by chance
For example:
So we‘ll choose one at random then.
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A collocate search in the iWeb corpus:
1 CHOSEN 4713 2 SELECTED 4295 3 TIMES 2328 4 DRAWN 1694 5 PICKED 1493 6 PICK 1155 7 WINNER 1068 8 ENTRIES 999 9 INTERVALS 928
10 WINNERS 707