Amal has 7 books and three of them are Maths books. He is going to arrange them on a book shelf. How many possible ways does Amal can arrange the books in a way that the three Maths books are in the same order and adjacent.



Question 8Answer

a.
120


b.
5040


c.
24


d.
720

To solve this problem, we need to determine the number of possible ways to arrange 7 books on a shelf such that three specific Maths books are adjacent and in a fixed order relative to each other.

### Step 1: Treat the 3 Maths Books as a Single Unit
Since the 3 Maths books must be adjacent and in the same order, we can treat them as a single unit. This reduces the problem to arranging 5 units (4 individual books + 1 unit of 3 Maths books).

### Step 2: Calculate the Number of Arrangements
The number of ways to arrange these 5 units on the shelf is the factorial of 5:

\[
5! = 5 \times 4 \times 3 \times 2 \times 1 = 120
\]

### Step 3: Consider the Fixed Order of the Maths Books
Since the 3 Maths books must be in a fixed order, there is only **1** way to arrange them within the unit.

### Final Calculation
Thus, the total number of ways to arrange all the books on the shelf, with the 3 Maths books being adjacent and in a fixed order, is:

\[
120 \times 1 = 120
\]

### Final Answer
The correct answer is:

\[
\boxed{120}
\]

Do you want details or have any questions?

Here are 5 related questions to expand your understanding:
1. What if the Maths books can be in any order, but still must remain adjacent?
2. How would the answer change if there were 8 books total and 4 were Maths books?
3. What if only 2 Maths books had to be adjacent, not 3?
4. How many ways can the 7 books be arranged if there are no restrictions on the Maths books?
5. How does the number of arrangements change if all the books are identical?

**Tip:** Factorials grow very quickly, so when calculating possible arrangements, always look for ways to simplify the problem, such as grouping items or reducing the total count.

Amal has 7 books and three of them are Maths books. He is going to arrange them on a book shelf. How many possible ways can Amal arrange the books in a way that the three Maths books are in the same order and adjacent?

Explore how to calculate the number of ways to arrange 7 books, ensuring that 3 Maths books remain adjacent and in the same order. This problem demonstrates key concepts in permutations, factorials, and combinatorics, suitable for students in Grades 9-10.

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