In how many ways can 5 different colored balls be arranged in a line?

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Question: In how many ways can 5 different colored balls be arranged in a line?

Options:

Correct Answer: 720

Solution:

The number of ways to arrange 5 different colored balls is 5! = 120.

In how many ways can 5 different colored balls be arranged in a line?

In how many ways can 5 different colored balls be arranged in a line?

Step 1: Understand that we have 5 different colored balls.
Step 2: Realize that arranging these balls means putting them in a specific order.
Step 3: Know that the number of ways to arrange 'n' different items is calculated using 'n factorial', written as 'n!'.
Step 4: For 5 balls, we need to calculate 5!. This means we multiply 5 by every whole number less than it down to 1.
Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1.
Step 6: Perform the multiplication: 5 × 4 = 20, then 20 × 3 = 60, then 60 × 2 = 120, and finally 120 × 1 = 120.
Step 7: Conclude that there are 120 different ways to arrange the 5 different colored balls.

Permutations – The arrangement of distinct objects in a specific order, calculated using factorial notation.