In how many ways can 6 different colored balls be arranged in a line?

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Question: In how many ways can 6 different colored balls be arranged in a line?

Options:

Correct Answer: 720

Solution:

The number of arrangements of 6 different colored balls is 6! = 720.

In how many ways can 6 different colored balls be arranged in a line?

In how many ways can 6 different colored balls be arranged in a line?

Step 1: Understand that we have 6 different colored balls.
Step 2: Realize that we want to arrange these balls in a line.
Step 3: Know that the number of ways to arrange 'n' different items is given by 'n factorial', written as 'n!'.
Step 4: For our case, 'n' is 6 because we have 6 balls.
Step 5: Calculate 6! (6 factorial), which means 6 × 5 × 4 × 3 × 2 × 1.
Step 6: Perform the multiplication: 6 × 5 = 30, then 30 × 4 = 120, then 120 × 3 = 360, then 360 × 2 = 720, and finally 720 × 1 = 720.
Step 7: Conclude that there are 720 different ways to arrange the 6 different colored balls in a line.

Permutations – The question tests the understanding of permutations, specifically how to arrange a set of distinct objects.