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In a group of 6 boys and 5 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?
Verified Answer
In a group of 6 boys and 5 girls, 5 students have to be selected. In h...
Answer – b) 1526 Explanation : 6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5
This question is part of UPSC exam. View all Quant courses
Most Upvoted Answer
In a group of 6 boys and 5 girls, 5 students have to be selected. In h...
Given:
- Group of 6 boys and 5 girls
- 5 students to be selected
- At least 2 boys should be included
To find: Number of ways to select 5 students
Approach:
We can use the principle of counting to find the number of ways to select 5 students. We can divide the problem into two cases:
1. When 2 boys and 3 girls are selected
2. When 3 boys and 2 girls are selected
Case 1:
Number of ways to select 2 boys from 6 boys = 6C2 = 15
Number of ways to select 3 girls from 5 girls = 5C3 = 10
Total number of ways to select 2 boys and 3 girls = 15 x 10 = 150
Case 2:
Number of ways to select 3 boys from 6 boys = 6C3 = 20
Number of ways to select 2 girls from 5 girls = 5C2 = 10
Total number of ways to select 3 boys and 2 girls = 20 x 10 = 200
Total number of ways to select 5 students with at least 2 boys = 150 + 200 = 350
Therefore, the correct option is (e) None of these as none of the options match the answer.
- Group of 6 boys and 5 girls
- 5 students to be selected
- At least 2 boys should be included
To find: Number of ways to select 5 students
Approach:
We can use the principle of counting to find the number of ways to select 5 students. We can divide the problem into two cases:
1. When 2 boys and 3 girls are selected
2. When 3 boys and 2 girls are selected
Case 1:
Number of ways to select 2 boys from 6 boys = 6C2 = 15
Number of ways to select 3 girls from 5 girls = 5C3 = 10
Total number of ways to select 2 boys and 3 girls = 15 x 10 = 150
Case 2:
Number of ways to select 3 boys from 6 boys = 6C3 = 20
Number of ways to select 2 girls from 5 girls = 5C2 = 10
Total number of ways to select 3 boys and 2 girls = 20 x 10 = 200
Total number of ways to select 5 students with at least 2 boys = 150 + 200 = 350
Therefore, the correct option is (e) None of these as none of the options match the answer.
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