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In how many ways can 4 different colored balls be arranged in a line?

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Question: In how many ways can 4 different colored balls be arranged in a line?

Options:

  1. 16
  2. 24
  3. 32
  4. 48

Correct Answer: 24

Solution: 

The number of arrangements is 4! = 24.

In how many ways can 4 different colored balls be arranged in a line?

Practice Questions

Q1
In how many ways can 4 different colored balls be arranged in a line?
  1. 16
  2. 24
  3. 32
  4. 48

Questions & Step-by-Step Solutions

In how many ways can 4 different colored balls be arranged in a line?
Correct Answer: 24
  • Step 1: Understand that we have 4 different colored balls.
  • Step 2: Realize that we want to arrange these 4 balls in a line.
  • Step 3: Know that the number of ways to arrange 'n' different items is given by 'n!'.
  • Step 4: Since we have 4 balls, we need to calculate 4!. This means 4 factorial.
  • Step 5: Calculate 4! = 4 × 3 × 2 × 1.
  • Step 6: Perform the multiplication: 4 × 3 = 12, then 12 × 2 = 24, and finally 24 × 1 = 24.
  • Step 7: Conclude that there are 24 different ways to arrange the 4 colored balls in a line.
  • Permutations – The arrangement of distinct objects in a specific order, calculated using factorial notation.
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