You are right about limited outfield spots on most Rosters, in fact, that is pretty much the case for all position players.
The greatest odds on is at the Pitcher position, as Mark B. stated.
Rosters of 35 will normally be comprised of near half pitchers; say 17 and 3 catchers. That leaves 15 position players remaining, about two per each field position. Those field positions will vary depending upon team needs and how successful their recruiting efforts are filled. If the kid hits they will determine where he best fits their needs. If he doesn't hit much he better be fast and or have a big time glove.