Question

A teacher has four books—A, B, C, and D—to assign to four students in any order he prefers.

Set S includes all possible arrangements of the four books.

Set X includes all possible arrangements when book C is chosen first and D is chosen second.

Which notation is correct?


If book C is chosen first and D is chosen second, in how many ways can the teacher assign the books?

Answer 1

Write S as the set of all permutations of {A,B,C,D}, and X as the subset of those permutations with C in position 1 and D in position 2. In symbols:

- S = {all permutations of A,B,C,D}, so |S| = 4! = 24.
- X = {σ ∈ S : σ(1)=C and σ(2)=D}.

With C and D fixed in the first two spots, the remaining two books (A and B) can be arranged in 2! = 2 ways (C D A B and C D B A). So there are 2 possible assignments.