Is this the correct way to do these questions

There are 40 students in a class, 10 from arts, 20 from maths and 10 from science. How many different groups of three students can be formed if each group must contain one student from each of the three areas?

10c1 = 10
20c1 = 20
10c1 = 10

Use the fundamental counting rule:

10x10x20 = 2000 ways to assign the students?

how many different groups of students can be formed if each group must consist of 1 arts student, 2 maths students and 1 science student?

10c1, 10c1, 20c2 = 10, 10, 190. Apply counting rule: 10x10x190 = 19000 ways to assign the students?

yes its perfect

I think the last one should be 10 x 380 x 10 = 38,000.