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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)424
- b)426
- c)440
- d)460
- 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 5 girls, 5 students have to be selected. In h...
Answer – b) 426 Explanation : 6c2*5c3 + 6c3*5c2 + 6c4*5c1 + 6c5
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In a group of 6 boys and 5 girls, 5 students have to be selected. In h...
Problem: 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?
Solution:
Total number of ways to select 5 students out of 11 = $^{11}C_5$ = 462
Number of ways to select 5 students which includes no boy = $^{5}C_5$ $*$ $^6C_0$ = 1
Number of ways to select 5 students which includes only one boy = $^{6}C_1$ $*$ $^5C_4$ = 30
Number of ways to select 5 students which includes at least 2 boys = Total number of ways to select 5 students - (number of ways to select 5 students which includes no boy + number of ways to select 5 students which includes only one boy)
= 462 - (1 + 30) = 431
Therefore, the number of ways to select 5 students which includes at least 2 boys is 431.
Answer: Option B (426)
Solution:
Total number of ways to select 5 students out of 11 = $^{11}C_5$ = 462
Number of ways to select 5 students which includes no boy = $^{5}C_5$ $*$ $^6C_0$ = 1
Number of ways to select 5 students which includes only one boy = $^{6}C_1$ $*$ $^5C_4$ = 30
Number of ways to select 5 students which includes at least 2 boys = Total number of ways to select 5 students - (number of ways to select 5 students which includes no boy + number of ways to select 5 students which includes only one boy)
= 462 - (1 + 30) = 431
Therefore, the number of ways to select 5 students which includes at least 2 boys is 431.
Answer: Option B (426)
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