Library Bookshelf Arrangement?
In a school library, there are eight books to be arranged on a bookshelf in a row. Five of the books are fiction and three are non-fiction. The fiction books are to be placed together, and the non-fiction books are to be placed together. In how many distinct ways can these eight books be arranged?
1 Answer
📌 CONCEPT: The problem involves arranging books on a bookshelf, where fiction and non-fiction books are to be placed together, and we need to find the number of distinct ways to arrange them.
📐 RULE / FORMULA: This problem can be solved using the concept of permutations of a set of objects, where we first treat the two groups of books (fiction and non-fiction) as single units, and then arrange these units, followed by arranging the books within each group.
💡 WORKED EXAMPLE: Consider arranging 3 non-fiction books and 5 fiction books. First, treat the non-fiction books as one unit and the fiction books as another unit. There are 2! ways to arrange these 2 units. Now, within the non-fiction group, there are 3! ways to arrange the 3 books, and within the fiction group, there are 5! ways to arrange the 5 books. So, the total number of arrangements is 2! * 3! * 5!.
⚠️ COMMON MISTAKE: Students often forget to account for the internal arrangements within each group, or they might not correctly apply the formula for permutations of a set of objects.
23 Jun 26
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