According to Study in India :: Why study in India ?, students hail from "Afghanistan, Bangladesh, Bhutan, Ethiopia, Fiji, France, Germany, Indonesia, Iran, Iraq, Japan, Jordan, Kenya, Lebanon, Madagascar, Malaysia, Mauritius, Myanmar, Nepal, Somalia, Sri Lanka, Surinam, Syria, Thailand, UK, US, Vietnam and Zimbabwe etc for their higher studies." There are many internship opportunities, which is exactly what I am looking for.
According to International Students in India, the number of international students in India during the 2011-2012 year was 33,151 students (both public and private institutions.) Here is a breakdown of the nationalities and percentages: Nepal 19%, Bhutan 8%, Iran 7%, Afghanistan 7%, Malaysia 5%, Sudan 5%, Iraq 5%, Sri Lanka 4%, the United States 3%, UAE 2%, with all others constituting the remaining percentages. I have yet to find out if those numbers reflect both undergraduate and postgraduate studies.
I read that Nepal and Bhutan constitute the largest percentages of foreign students. The United States was relatively low on the list. I had posted these static, but because of the link I'd added, that post hasn't been approved yet.