Problem

Source: 2013 Saudi Arabia Pre-TST 1.3

Tags: combinatorics



Ten students take a test consisting of $4$ different papers in Algebra, Geometry, Number Theory and Combinatorics. First, the proctor distributes randomly the Algebra paper to each student. Then the remaining papers are distributed one at a time in the following order: Geometry, Number Theory, Combinatorics in such a way that no student receives a paper before he finishes the previous one. In how many ways can the proctor distribute the test papers given that a student may for example nish the Number Theory paper before another student receives the Geometry paper, and that he receives the Combinatorics paper after that the same other student receives the Combinatorics papers.