How many ways can 5 different colored balls be arranged in a line? (2016)

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Question: How many ways can 5 different colored balls be arranged in a line? (2016)

Options:

Correct Answer: 120

Exam Year: 2016

Solution:

The number of arrangements of 5 different colored balls is 5! = 120.

How many ways can 5 different colored balls be arranged in a line? (2016)

How many ways can 5 different colored balls be arranged in a line? (2016)

Step 1: Understand that we have 5 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!' (n factorial).
Step 4: Calculate 5! (5 factorial), which means 5 x 4 x 3 x 2 x 1.
Step 5: Perform the multiplication: 5 x 4 = 20, then 20 x 3 = 60, then 60 x 2 = 120, and finally 120 x 1 = 120.
Step 6: Conclude that there are 120 different ways to arrange the 5 colored balls.

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