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
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
