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Question
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
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Solution
The correct option is B 3!
There are two ways this problem can be interpreted, but thankfully, the answer doesn't depends on that interpretation.
This is because we're only asked for the ordering of the books A,B and E and all of the ambiguity comes from how C and D are treated.
In placing books A,B and E, we have three ways to pick the first book.
Once we've placed that book on the shelf, we can't place it again, leaving two options for the second book.
When that book is placed on the shelf, we have only one left, so there's one final option for the last book.
When we write this product, note that we can simplify it to a factorial.⇒ 3×2×1=3!
There are two ways this problem can be interpreted, but thankfully, the answer doesn't depends on that interpretation.
This is because we're only asked for the ordering of the books A,B and E and all of the ambiguity comes from how C and D are treated.
In placing books A,B and E, we have three ways to pick the first book.
Once we've placed that book on the shelf, we can't place it again, leaving two options for the second book.
When that book is placed on the shelf, we have only one left, so there's one final option for the last book.
When we write this product, note that we can simplify it to a factorial.
⇒ 3×2×1=3!
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