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

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

Options:

  1. 60
  2. 120
  3. 100
  4. 80

Correct Answer: 120

Solution: 

The number of arrangements is 5! = 120.

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

Practice Questions

Q1
In how many ways can 5 different colored balls be arranged in a box?
  1. 60
  2. 120
  3. 100
  4. 80

Questions & Step-by-Step Solutions

In how many ways can 5 different colored balls be arranged in a box?
Correct Answer: 120
  • Step 1: Understand that we have 5 different colored balls.
  • Step 2: Realize that we want to find out how many different ways we can arrange these 5 balls.
  • Step 3: Know that the number of arrangements of 'n' different items is calculated using the factorial of 'n', which is written as 'n!'.
  • Step 4: For our case, 'n' is 5 because we have 5 balls. So we need to calculate 5!.
  • Step 5: Calculate 5! by multiplying all whole numbers from 1 to 5: 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 question tests the understanding of permutations, specifically how to arrange a set of distinct objects.
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