NCERT Class XI Mathematics - Permutations and Combinations - Solutions
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Question : 33
Total: 41
A committee of 7 has to be formed from 9 boys and 4 girls. In how many ways can this be done when the committee consists of
(i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?
(i) exactly 3 girls ? (ii) atleast 3 girls ? (iii) atmost 3 girls ?
Solution:
(i) When committee consists of exactly 3 girls. Then remaining will be 4 boys in the committee.
So the required no. of ways =
C 4 ×
C 3
×
(ii) When committee consists of atleast 3 girls i.e., it may be 3 girls or 4 girls. Then there are two cases. One when there are 3 girls in a committee, then the boys will be 4 & second when there are 4 girls in a committee, then the boys will be 3. So,
No. of ways in first case =
C 3 ×
C 4
No. of ways in second case =
C 4 ×
C 3
\ Required no. of ways =
C 3 ×
C 4 +
C 4 ×
C 3
(iii) When atmost 3 girls are there in committee.
Total no. of people = 13, No. of people in committee = 7.
No. of ways of 7 people out of 13 people =
C 7
When 4 girls are in committee, then no. of ways =
C 4 ×
C 3
So the required no. of ways = 1716 – 84 = 1632
So the required no. of ways =
(ii) When committee consists of atleast 3 girls i.e., it may be 3 girls or 4 girls. Then there are two cases. One when there are 3 girls in a committee, then the boys will be 4 & second when there are 4 girls in a committee, then the boys will be 3. So,
No. of ways in first case =
No. of ways in second case =
\ Required no. of ways =
(iii) When atmost 3 girls are there in committee.
Total no. of people = 13, No. of people in committee = 7.
No. of ways of 7 people out of 13 people =
When 4 girls are in committee, then no. of ways =
So the required no. of ways = 1716 – 84 = 1632
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