A college student purchase 10 posters for her dorm room but she only has space to hang six of them how many specific ways can student arrange and hang these six posters on her wall

This is a question of arrangement of the posters. In this regard, ordering becomes very critical.

Therefore, permutation is the most applicable concept. That is,

Specific number of ways to arrange 6 out 10 posters = 10P6 = 10! / (10-6) ! = 151,200 ways.