How many different ways can you arrange 5 different colored balls in a row?

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Question: How many different ways can you arrange 5 different colored balls in a row?

Options:

Correct Answer: 720

Solution:

The number of arrangements of 5 balls is 5! = 5 × 4 × 3 × 2 × 1 = 120.

How many different ways can you arrange 5 different colored balls in a row?

How many different ways can you arrange 5 different colored balls in a row?

Step 1: Understand that you have 5 different colored balls.
Step 2: Realize that you want to arrange these balls in a row.
Step 3: Know that the number of ways to arrange 'n' different items is given by 'n!'.
Step 4: For 5 balls, you will calculate 5! (which means 5 factorial).
Step 5: Calculate 5! by multiplying the numbers from 5 down to 1: 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 in a row.

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