Q. 30 B5.0( 1 Vote )

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 :

at least 3 girls?

Answer :

Given that we need to select 7 members out of 9 boys and 4 girls by following the conditions:


i. exactly 3 girls


ii. at least 3 girls


iii. at most 3 girls.


It is told we need to select 7 members out of 9 boys and 4 girls with at least 3 girls.


The possible cases are the following:


i. Selecting 3 girls and 4 boys


ii. Selecting 4 girls and 3 boys


Let us assume the no. of ways of selecting is N1.


N1 = ((no. of ways of selecting 3 girls out of 4 girls) × (no. of ways of selecting 4 boys out of 9 boys)) × ((no. of ways of selecting 4 girls out of 4 girls) × (no. of ways of selecting 3 boys out of 9 boys))


N1 = ((4C3) × (9C4)) + ((4C4) × (9C3))


We know that ,


And also n! = (n)(n – 1)......2.1





N1 = (4 × 126) + (1 × 84)


N1 = 504 + 84


N1 = 588


The no. of ways of selecting 7 members with at least 3 girls is 588.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Lecture on Combinations49 mins
Combinations - BOX & GAP Method38 mins
Check Your progress Part 2| Interactive Quiz: Permutation & CombinationFREE Class
Understand Permutations like never before60 mins
Interactive Quiz on Combinations50 mins
Interactive Quiz on Combinations-02FREE Class
Circular permutationsFREE Class
Lets see how good you can manage numbers | P&C Quiz Challenge41 mins
Ladoo Bhikhari Concept46 mins
Indepth Understanding of Factorials56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :