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In a group of 6 boys and 8 girls, 5 students have to be selected. In how many ways it can be done so that at least 2 boys are included
- a)1524
- b)1526
- c)1540
- d)1560
- e)None of these
Correct answer is option 'B'. Can you explain this answer?
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In a group of 6 boys and 8 girls, 5 students have to be selected. In h...
Answer – b) 1526 Explanation : 6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5
Most Upvoted Answer
In a group of 6 boys and 8 girls, 5 students have to be selected. In h...
Solution:
Total number of ways to select 5 students from 14 students = 14C5 = 2002
Number of ways to select 5 students with no boys = 8C5 = 56
Number of ways to select 5 students with only 1 boy = 6C1 × 8C4 = 840
Therefore, the number of ways to select 5 students with at least 2 boys = 2002 - 56 - 840 = 1106
Alternate solution:
Number of ways to select 5 students with at least 2 boys
= Number of ways to select 2 boys and 3 students from remaining 12 students
+ Number of ways to select 3 boys and 2 students from remaining 12 students
= 6C2 × 12C3 + 6C3 × 12C2 = 1526
Therefore, the correct answer is option B (1526).
Total number of ways to select 5 students from 14 students = 14C5 = 2002
Number of ways to select 5 students with no boys = 8C5 = 56
Number of ways to select 5 students with only 1 boy = 6C1 × 8C4 = 840
Therefore, the number of ways to select 5 students with at least 2 boys = 2002 - 56 - 840 = 1106
Alternate solution:
Number of ways to select 5 students with at least 2 boys
= Number of ways to select 2 boys and 3 students from remaining 12 students
+ Number of ways to select 3 boys and 2 students from remaining 12 students
= 6C2 × 12C3 + 6C3 × 12C2 = 1526
Therefore, the correct answer is option B (1526).
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