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In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

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Question: In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

Options:

  1. 60
  2. 40
  3. 20
  4. 30

Correct Answer: 60

Solution: 

The number of ways to select 2 boys from 5 is C(5, 2) and 2 girls from 4 is C(4, 2). Total = C(5, 2) * C(4, 2) = 10 * 6 = 60.

In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?

Practice Questions

Q1
In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
  1. 60
  2. 40
  3. 20
  4. 30

Questions & Step-by-Step Solutions

In how many ways can 2 boys and 2 girls be selected from 5 boys and 4 girls?
Correct Answer: 60
  • Step 1: Identify the total number of boys and girls. We have 5 boys and 4 girls.
  • Step 2: Determine how many boys we need to select. We need to select 2 boys.
  • Step 3: Use the combination formula to find the number of ways to select 2 boys from 5. This is represented as C(5, 2).
  • Step 4: Calculate C(5, 2). The formula for combinations is C(n, r) = n! / (r! * (n - r)!). So, C(5, 2) = 5! / (2! * (5 - 2)!) = 10.
  • Step 5: Now, determine how many girls we need to select. We need to select 2 girls.
  • Step 6: Use the combination formula to find the number of ways to select 2 girls from 4. This is represented as C(4, 2).
  • Step 7: Calculate C(4, 2). Using the combination formula, C(4, 2) = 4! / (2! * (4 - 2)!) = 6.
  • Step 8: Multiply the number of ways to select boys by the number of ways to select girls. Total = C(5, 2) * C(4, 2) = 10 * 6.
  • Step 9: Calculate the total. 10 * 6 = 60.
  • Step 10: Conclude that there are 60 different ways to select 2 boys and 2 girls.
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