In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be displayed at a time?

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Q: In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be displayed at a time?

Solution: The number of ways to select and arrange 3 books from 5 is 5P3 = 60.

Steps: 9

Step 1: Understand that we have 5 different books.
Step 2: We need to select 3 books from these 5 books.
Step 3: Realize that the order in which we arrange the 3 selected books matters.
Step 4: Use the formula for permutations to find the number of ways to arrange the books. The formula is nPr = n! / (n - r)!, where n is the total number of items (books) and r is the number of items to arrange.
Step 5: In this case, n = 5 (the total books) and r = 3 (the books we want to arrange).
Step 6: Calculate 5P3 using the formula: 5P3 = 5! / (5 - 3)! = 5! / 2!.
Step 7: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120 and 2! = 2 × 1 = 2.
Step 8: Now divide: 120 / 2 = 60.
Step 9: Therefore, the number of ways to select and arrange 3 books from 5 is 60.