Chances for Berkeley and Caltech CS

Hi! I really want to go to UC Berkeley for computer science (B.A, not B.S. because EECS is too difficult to get into and I want more freedom to explore). I am also applying to Caltech for computer science. I am a female.

GPA: 4.6 (weighted 10-12), 3.93 (UW 10-12)
SAT: 2310 (800 math, 800 CR, 710 writing) SAT subject: math II 770, chem 770, bio 760

classes:
16 APs including entire senior year
AP Stats, math up to AP Calc BC
took computer programming course at community college over summer

ECs and awards:
National AP Scholar
6th place in UCSD Statistics Competition (not even sure if I should put this on app…)
company member of Scripps Ballet Theatre (youth ballet company) for 3 years
16-25 hours a week of dance (dancing since age 11)
co-president and founder of food and community service club, just started this January
probably nearly 300 volunteer hours
volunteered at hospital and sports medicine clinic
started food blog

let me know if you need more information and thank you so much!

Why Caltech and Berkeley? The schools are vastly different. If you think EECS is too difficult to get into why would Caltech be any easier - anything below a 790 on the Math 2 exam is bottom quartile.

Where is the background in computer science? Am I missing something here?