In how many ways can 7 different books be arranged if 3 specific books must be o

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

Options:

Correct Answer: 720

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.

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

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.

Permutations – The arrangement of items in a specific order, where the order matters.
Factorial – The product of all positive integers up to a given number, used to calculate arrangements.
Conditional Arrangement – Arranging items with specific conditions, such as certain items needing to be in a particular position.