In how many ways can 6 different colored balls be arranged in a row? (2018)

In how many ways can 6 different colored balls be arranged in a row? (2018)

Step 1: Understand that we have 6 different colored balls.
Step 2: Recognize that we want to arrange these balls in a row.
Step 3: Realize that the order of the balls matters because they are different colors.
Step 4: 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 5: For 6 balls, we calculate 6! which means 6 x 5 x 4 x 3 x 2 x 1.
Step 6: Perform the multiplication: 6 x 5 = 30, then 30 x 4 = 120, then 120 x 3 = 360, then 360 x 2 = 720, and finally 720 x 1 = 720.
Step 7: Conclude that there are 720 different ways to arrange the 6 different colored balls.

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