Question

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Five different books (A, B, C, D and E) are to be arranged on a shelf. Books C and D are to be arranged first and second starting from the right of the shelf. The number of different orders in which books A, B, and E may be arranged is?

Answer 1

So books C and D will always be in the same position on the right of the shelf, either as xxxCD or xxxDC, but when we are talking about the order in which books A, B, and E can be in, they have to stay on the left side (replacing the x’s shown above) and the orders you can put them in are:

ABE
AEB
BEA
BAE
EAB
EBA

So any of the combinations above including A, B, and E can replace the x’s is xxxCD or xxxDC

Answer 2

1. C,D, A,B,E
2. C,D, A,E,B

3. C,D, E,A,B
4. C,D, E,B,A

5. C,D, B,A,E
6. C,D, B,E,A

There are 6 different ways in which you can put the books in order.