The correct sentence is:
Each of the students' textbooks has been carefully covered to protect the binding.
Step-by-step explanation:
"Why is Melody and Sam playing in the rain?" should be corrected to "Why are Melody and Sam playing in the rain?" The subject "Melody and Sam" is plural, so the verb should be "are" instead of "is."
"The little fuzz balls all over my new sweater looks like balls of lint." should be corrected to "The little fuzz balls all over my new sweater look like balls of lint." The subject "fuzz balls" is plural, so the verb should be "look" instead of "looks."
"One of my housemates are always leaving dirty dishes in the sink." should be corrected to "One of my housemates is always leaving dirty dishes in the sink." The subject "one" is singular, so the verb should be "is" instead of "are."
I hope this helped!
~~~Harsha~~~