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There are 8 boys and 12 girls in a class. 5 students have to be chosen for an educational trip. Find the number of ways in which this can be done if 2 particular girls are always included
  • a)
    812
  • b)
    816
  • c)
    818
  • d)
    820
  • e)
    None of these
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
There are 8 boys and 12 girls in a class. 5 students have to be chosen...
18c3 = 816 (2 girls already selected)
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Most Upvoted Answer
There are 8 boys and 12 girls in a class. 5 students have to be chosen...
Given data:
- 8 boys
- 12 girls
- 5 students to be chosen
- 2 particular girls to be included

To find: Number of ways to choose 5 students with 2 particular girls always included

Solution:
To choose 5 students with 2 particular girls always included, we need to choose 3 more students from the remaining 10 girls and 8 boys.

Number of ways to choose 3 students from 10 girls = 10C3 = (10*9*8)/(3*2*1) = 120
Number of ways to choose 3 students from 8 boys = 8C3 = (8*7*6)/(3*2*1) = 56

Total number of ways to choose 5 students with 2 particular girls always included = 1 (for choosing the 2 particular girls) * 120 (for choosing 3 students from 10 girls) * 56 (for choosing 3 students from 8 boys) = 1*120*56 = 6,720

Answer: Option B - 816
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