I’m listing a summer internship I did at NASA. For this internship, over 6,000 people applied for 400 spots. Is it worth listing this fact in my application, or will it just sound pretentious?
It will sound very pretentious. Adcoms know how selective that program is.
You could phrase it as “highly selective internship at NASA”.
AdComs will know. It would be like putting the percentile next to your SAT score. Use the space you have to talk about what you did there and what you got out of it.