In how many ways can 7 different books be arranged if 3 specific books must be o
Practice Questions
Q1
In how many ways can 7 different books be arranged if 3 specific books must be on the top?
720
120
5040
840
Questions & Step-by-Step Solutions
In how many ways can 7 different books be arranged if 3 specific books must be on the top?
Correct Answer: 144
Step 1: Identify the 3 specific books that must be on the top. Let's call them Book A, Book B, and Book C.
Step 2: Calculate the number of ways to arrange these 3 specific books. Since they are different, we can arrange them in 3! (3 factorial) ways. 3! = 3 × 2 × 1 = 6.
Step 3: Now, we have 4 remaining books that can be arranged freely. Let's call them Book D, Book E, Book F, and Book G.
Step 4: Calculate the number of ways to arrange these 4 remaining books. Since they are also different, we can arrange them in 4! (4 factorial) ways. 4! = 4 × 3 × 2 × 1 = 24.
Step 5: To find the total number of arrangements, multiply the number of ways to arrange the 3 specific books by the number of ways to arrange the 4 remaining books. Total = 6 (ways to arrange the top books) × 24 (ways to arrange the remaining books) = 144.
