Probably 17 or 18, maybe more if there are a bunch of missionaries. Right now most of Utah's 8 commits are from Texas (Parks, Gentry, Ford, Renfro, Faloona) where BYU doesn't recruit often.

I'm a little surprised no BYU offer for Kamo'i Latu (Hawaii kid), but other than him and Wegis (CA) the rest of Utah's commits don't seem like kids that BYU would be looking at.

There are likely to be several Utes with BYU offers in the near future (none of these are committed yet, but all are "leaning" Utah):

TE Alex Lines (AZ)
OT Solatoa Moea'i (HI)
OT Alex Harrison (UT)
LB Nate Ritchie (UT)

DT Keanu Tanuvasa (CA) is still up in the air, I'm not sure where he's headed. Same with LB Tate Romney (AZ), but BYU is more likely than Utah (for obvious reasons)

I'm also surprised no offers for three of the top Utah HS kids: DE Van Fillinger, DE Xavier Carlton, and LB Sione Fotu. All three are probable Utes (although, like the four listed above, none are certain).