In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?
Practice Questions
1 question
Q1
In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?
60
120
30
90
The number of ways to select and arrange 3 books from 5 is P(5, 3) = 5! / (5-3)! = 60.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 5 different books be selected and arranged on a shelf if only 3 can be placed?
Solution: The number of ways to select and arrange 3 books from 5 is P(5, 3) = 5! / (5-3)! = 60.
Steps: 7
Step 1: Understand that we have 5 different books and we want to select 3 of them.
Step 2: Recognize that the order in which we arrange the books matters.
Step 3: Use the formula for permutations, which is P(n, r) = n! / (n - r)!. Here, n is the total number of items (5 books) and r is the number of items to arrange (3 books).
Step 4: Plug in the values into the formula: P(5, 3) = 5! / (5 - 3)!.
Step 5: Calculate 5! (which is 5 x 4 x 3 x 2 x 1 = 120) and (5 - 3)! (which is 2! = 2 x 1 = 2).
Step 6: Divide the results: 120 / 2 = 60.
Step 7: Conclude that there are 60 different ways to select and arrange 3 books from 5.
