Assume 7 students are assigned into 3 indistinguishable offices. How many ways can this happen under each condition?

1. assign students into groups of 1, 1, and 5, which means 2 students have their own offices, and the ways can other 5 share an office.

2.assign students into groups of 1, 2, and 4

3.assign students into groups of 1, 3, and 3

4.assign students into groups of 2, 2, and 3