If 4 different books are to be arranged on a shelf, how many arrangements are po
Practice Questions
Q1
If 4 different books are to be arranged on a shelf, how many arrangements are possible?
16
24
32
48
Questions & Step-by-Step Solutions
If 4 different books are to be arranged on a shelf, how many 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 (written as n!) is the product of all positive integers up to n.
Step 4: For 4 books, we calculate 4! (4 factorial). This means we multiply 4 × 3 × 2 × 1.
Step 5: Calculate 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 factorial (n!) is used to determine the number of ways to arrange n distinct items.
Permutations – This problem tests the understanding of permutations, where the order of arrangement matters.
