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9. [Maximum mark: 7]
   A teacher takes $n$ students on a field trip. The students are assigned randomly into two groups.

(a) Write down an expression for the number of ways that the students could be assigned.

Two of the students ask the teacher not to work in the same group. The teacher agrees and now finds that the number of ways to assign the students is halved.

(b) Determine the value of $n$.