At Flordyce University any student who wants to participate in a certain archaeological dig is eligible to do so but only if the student has taken at least one archaeology course and has shown an interest in the field. Many students who have shown an interest in archaeology never take even one archaeology course. Therefore, many students who want to participate in the dig will be ineligible to do so.
My take -
For a student to be eligible for participating in arch dig = he/she must have taken at least one course AND must have shown interest in the field. (Premise 1)
Many students who have shown interest in archaeology have never taken even one arch course (Premise 2)
The passage concludes - therefore MANY students who want to participate in the dig will be ineligible to do so
Clearly it must be assumed that these many students who are interested in arch but have never taken a course would WANT to participate in the dig. Only then would the argument that MANY STUDENTS
WHO WANT TO PARTICIPATE IN THE DIG would be ineligible hold true.
On the contrary it is still possible that those who have applied to participate in the dig qualify completely for the expedition (even though they may form a minority when compared with the total strength of the students)