In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?
Practice Questions
1 question
Q1
In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?
48
120
60
24
Treat the 2 specific books as one unit. Then, we have 4 units to arrange: 4! × 2! = 48.
Questions & Step-by-step Solutions
1 item
Q
Q: In how many ways can 5 different books be arranged on a shelf if 2 specific books must be together?
Solution: Treat the 2 specific books as one unit. Then, we have 4 units to arrange: 4! × 2! = 48.
Steps: 7
Step 1: Identify the 2 specific books that must be together. Let's call them Book A and Book B.
Step 2: Since Book A and Book B must be together, treat them as one single unit or 'block'.
Step 3: Now, instead of 5 separate books, you have 4 units to arrange: the 'block' (Book A and Book B together) and the other 3 individual books.
Step 4: Calculate the number of ways to arrange these 4 units. This is done using the factorial of the number of units: 4! (which is 4 × 3 × 2 × 1 = 24).
Step 5: Next, consider the arrangement of the 2 books within the 'block'. There are 2! ways to arrange Book A and Book B (which is 2 × 1 = 2).
Step 6: Multiply the number of arrangements of the 4 units by the arrangements of the 2 books in the block: 4! × 2! = 24 × 2 = 48.
Step 7: Therefore, the total number of ways to arrange the 5 books with the 2 specific books together is 48.
