JAMIA 2025 — Mathematics PYQ

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Question

JAMIA 2025 — Mathematics PYQ

JAMIA | Mathematics | 2025

How many ways can 4 books be arranged on a shelf?

Choose the correct answer:

Explanation

Solution

1. Using the Multiplication Principle:

When arranging 4 books, we have 4 positions to fill:

For the first position, we have 4 choices (any of the 4 books).
For the second position, we have 3 choices remaining.
For the third position, we have 2 choices remaining.
For the fourth position, we have 1 choice remaining.

The total number of arrangements is the product of these choices:

4 \times 3 \times 2 \times 1 = 24

2. Using the Factorial Formula:

The number of ways to arrange $n$ distinct objects in a row is given by $n!$ (n-factorial). Here, $n = 4$ .

The formula is:

\text{Total arrangements} = n!

Substituting $n = 4$ :

4! = 4 \times 3 \times 2 \times 1

4! = 24