If 4 different books are to be arranged on a shelf, how many different arrangeme

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Question: If 4 different books are to be arranged on a shelf, how many different arrangements are possible?

Options:

Correct Answer: 24

Solution:

The number of arrangements of 4 distinct books is 4! = 24.

If 4 different books are to be arranged on a shelf, how many different arrangements are possible?

If 4 different books are to be arranged on a shelf, how many different arrangements are possible?

Step 1: Understand that we have 4 different books to arrange.
Step 2: Recognize that the order in which we arrange the books matters.
Step 3: Use the factorial notation to calculate the number of arrangements. The factorial of a number (n!) means multiplying that number by all the whole numbers less than it down to 1.
Step 4: For 4 books, we calculate 4! (4 factorial). This means: 4! = 4 × 3 × 2 × 1.
Step 5: Perform the multiplication: 4 × 3 = 12, then 12 × 2 = 24, and finally 24 × 1 = 24.
Step 6: Conclude that there are 24 different ways to arrange the 4 books on the shelf.

Factorial – The concept of arranging distinct items is calculated using factorial notation, where n! (n factorial) represents the product of all positive integers up to n.