In how many ways can 7 different books be arranged if 3 specific books must be on the top?

1 question

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Q: In how many ways can 7 different books be arranged if 3 specific books must be on the top?

Solution: The 3 specific books can be arranged in 3! = 6 ways. The remaining 4 books can be arranged in 4! = 24 ways. Total = 6 * 24 = 144.

Steps: 5

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.