Read the following passage and solve the questions based on it.
There are five specializations—Marketing, Finance, Pro- duction, Personnel and Systems—available at the IIM. It is necessary for all students to take up a combination of at least two of the above specializations.
Based on common preferences, pre-set combinations called modules are offered, which are coded S001, S002, S003, S004 and S005. Each of these modules has two specializations, so that every specialization is assigned to two modules. Further, to allow for uncommon preferences a student is allowed to take up more than one combination in such a way that the specialization common to the two modules is dropped.
However, a student can specialize in more than two subjects by manipulating the combination of modules.
Additional information is as follows:
S001 has not been assigned to Production. S003 has not been assigned to Marketing. S004 has not been assigned to Finance. By choosing S001 and S003, one may specialize in Marketing and Systems. By choosing S001 and S002 one may specialize in Marketing, Production, Finance and Personnel. By choosing S001 and S004 one may specialize in Finance and Personnel.
Which of the following number of specializations is impossible for any student to take?