Final answer:
Ian can line up the textbooks in 6 different ways on his bookshelf.
Step-by-step explanation:
To determine the number of different ways Ian can line up the textbooks on his bookshelf, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order.
Since Ian has 3 textbooks, he can arrange them in 3! (3 factorial) ways.
This means that the number of different ways Ian can line up the textbooks on his bookshelf is 3! = 3 x 2 x 1 = 6.