How many firms should I apply to?
The short answer: as many applications as you can manage to complete in an application cycle, that are tailored, high-quality, and have been thoroughly checked for spelling and grammatical errors.
The better answer: At least 15-20 applications, which are tailored, high-quality quality and have been thoroughly checked for typos.
I recommend at least 15 because even stellar candidates will receive rejections. We have all heard of the trainee who applied to two firms and got offers from both but that’s rare. Most candidates, even those who receive multiple training contract and vacation scheme offers, receive far more rejections than offers. So by sending in at least 15 applications, you increase your odds dramatically than only sending in a handful.
Quality is always better than quantity. If you can only submit 10 high-quality applications before firm deadlines, that is a far better strategy than submitting 30-40 generic, badly written, riddled with typos applications.