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
exactly 3 girls
at most 3 girls
there are 9 boys and 4 girls. committee has 7 students.
(i) committee has exactly 3 girls.
therefore we can choose 3 girls out of 4 girls in ways
and we can choose remaining 4 candidates from 9 boys in ways.
thus the number of ways in which committee has exactly 3 girls =
(ii) committee has at most 3 girls.
total number of students = 9+4=13
total number of ways of selecting 7 members =
at most 3 girls , therefore committee has either 0,1,2,or 3 girls.
the number of ways that committee has girls more than 3 is 4 girls and 3 boys
thus the number of ways that committee has at most 3 girls
= total number of ways - the number of ways that committee has girls more than 3.
= 1716 - 84
=1632
hope this helps you.
(i) committee has exactly 3 girls.
therefore we can choose 3 girls out of 4 girls in ways
and we can choose remaining 4 candidates from 9 boys in ways.
thus the number of ways in which committee has exactly 3 girls =
(ii) committee has at most 3 girls.
total number of students = 9+4=13
total number of ways of selecting 7 members =
at most 3 girls , therefore committee has either 0,1,2,or 3 girls.
the number of ways that committee has girls more than 3 is 4 girls and 3 boys
thus the number of ways that committee has at most 3 girls
= total number of ways - the number of ways that committee has girls more than 3.
= 1716 - 84
=1632
hope this helps you.