How many ways can 4 different colored balls be arranged in a row?

How many ways can 4 different colored balls be arranged in a row?

Correct Answer: 24

Step 1: Understand that we have 4 different colored balls. Let's call them Ball A, Ball B, Ball C, and Ball D.
Step 2: Realize that when arranging these balls, the order matters. This means that Ball A in the first position and Ball B in the second position is different from Ball B in the first position and Ball A in the second position.
Step 3: To find the total number of arrangements, we use the factorial notation. The factorial of a number (n!) means multiplying that number by every whole number less than it down to 1.
Step 4: For 4 balls, we calculate 4! (which means 4 factorial). This is calculated as: 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 different colored balls in a row.

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