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In how many ways can 3 boys and 2 girls be seated in a row?

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Question: In how many ways can 3 boys and 2 girls be seated in a row?

Options:

  1. 30
  2. 60
  3. 120
  4. 24

Correct Answer: 60

Solution: 

The total number of arrangements is (3+2)! = 5! = 120.

In how many ways can 3 boys and 2 girls be seated in a row?

Practice Questions

Q1
In how many ways can 3 boys and 2 girls be seated in a row?
  1. 30
  2. 60
  3. 120
  4. 24

Questions & Step-by-Step Solutions

In how many ways can 3 boys and 2 girls be seated in a row?
Correct Answer: 120
  • Step 1: Identify the total number of people to be seated. We have 3 boys and 2 girls, which makes a total of 3 + 2 = 5 people.
  • Step 2: Understand that we need to find the number of ways to arrange these 5 people in a row.
  • Step 3: Use the factorial notation to calculate the arrangements. The number of ways to arrange n people is given by n! (n factorial).
  • Step 4: Since we have 5 people, we calculate 5! (5 factorial).
  • Step 5: Calculate 5! = 5 × 4 × 3 × 2 × 1 = 120.
  • Step 6: Conclude that there are 120 different ways to seat 3 boys and 2 girls in a row.
  • Permutations – The question tests the understanding of permutations, specifically how to arrange a set of distinct objects in a sequence.
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