100 students, 32 oral groups. If I write reports for half the students in the group (50), what's the probability I will end up writing a report for at least someone in each oral group?

I’m teaching a literature course, and my brain is a little bored from marking essays and journals and orals so this is to wake myself up.

I have 100 students in the class. Each of these students have 3 graded components: essay, journal, oral. For orals they are split into 32 oral groups (as evenly distributed as possible, with 3–4 students each).

I am responsible for writing full reports for half of the students (50).
What is the probability that I will write a report from at least someone from each of the 16 groups?

This is important because I’ve just been asked by my colleague to write the paragraph about oral assessment for the other half of the class. Now since the oral work is assessed by group, they argued that I can cut and paste large chunks of the same paragraph (or at least, not watch the same video again), thus reducing the workload. ... so, how many more completely brand new unmarked oral assessment videos will I have to expect to rewatch to write about?