A team has finished a game with 17-9 singles and extra-base hits 2 times since 1897, most recently Chicago White Sox on 11 September 1936. That is about one every 221,502 team-games.
Box score for the most recent one ↗
17-3 17-4 17-5 17-6 17-7 17-8 17-9 17-10 17-11 17-12 18-0 18-1 18-2
The whole distribution — Singles and Extra-Base Hits · All 18 shapes