Question

at an annual college science conference student presentations are scheduled one after another this year 5 students are presenting in bio, 5 in chem, and 2 in physics; in how many ways can the presentations be scheduled so that each subject is grouped together

Answer 1

The bio students can be arranged in (5 · 4 · 3 · 2 · 1) = 120 different ways.
For each of those . . .
The chem students can be arranged in (5 · 4 · 3 · 2 · 1) = 120 different ways.
For each of those . . .
The physics students can be arranged in (2 · 1) different ways.
For each of those . . .
The subjects can be arranged in (3 · 2 · 1) = 6 different ways.

The whole incredibly boring line-up of presentations
can be arranged in

(120 · 120 · 2 · 6) = 172,800 different ways .