How many ways can 8 different books be arranged on a shelf if 3 specific books m

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Question: How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?

Options:

Correct Answer: 5040

Solution:

Treat the 3 specific books as one unit. So, we have 6 units to arrange: 6! = 720. The 3 books can be arranged in 3! = 6 ways. Total = 720 * 6 = 4320.

How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?

How many ways can 8 different books be arranged on a shelf if 3 specific books must be together?

Step 1: Identify the 3 specific books that must be together. Let's call them A, B, and C.
Step 2: Treat the 3 specific books (A, B, C) as one single unit or block. Now, instead of 8 books, we have 6 units to arrange: the block (A, B, C) and the other 5 individual books.
Step 3: Calculate the number of ways to arrange these 6 units. This is done using the factorial of 6, which is 6! = 720.
Step 4: Now, calculate the number of ways to arrange the 3 specific books (A, B, C) within their block. This is done using the factorial of 3, which is 3! = 6.
Step 5: Multiply the number of arrangements of the 6 units by the number of arrangements of the 3 specific books. So, 720 (arrangements of units) * 6 (arrangements of A, B, C) = 4320.
Step 6: The final answer is 4320, which is the total number of ways to arrange the 8 books with the 3 specific books together.

Permutations – The arrangement of items in a specific order, considering the order of arrangement.
Grouping – Treating a set of items as a single unit to simplify the arrangement process.