Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A committee of 6 people needs to be selected from a group of 12 individuals, including 4 men and 6 women. If at least 3 women must be on the committee, how many different

A committee of 6 people needs to be selected from a group of 12 individuals, including 4 men and 6 women. If at least 3 women must be on the committee, how many different committees can be formed?

 

Option: 1

121


Option: 2

171


Option: 3

152


Option: 4

200


Answers (1)

best_answer

To calculate the number of different committees that can be formed, where at least 3 women must be on the committee, we can consider different scenarios based on the number of women on the committee.

Case 1: Selecting 3 women and 3 men:

The number of ways to select 3 women from 6 women is given by \mathrm{C(6,3)=20}

The number of ways to select 3 men from 4 men is given by \mathrm{C(4,3)=4.}

The total number of committees in this case is \mathrm{20 \times 4=80.}

Case 2: Selecting 4 women and 2 men:

The number of ways to select 4 women from 6 women is given by \mathrm{C(6,4)=15.}

The number of ways to select 2 men from 4 men is given by \mathrm{C(4,2)=6.}

The total number of committees in this case is \mathrm{15 \times 6=90.}

Case 3: Selecting all 6 women:

The number of ways to select 6 women from 6 women is given by \mathrm{C(6,6)=1.}

To find the total number of committees that satisfy the given condition, we sum up the number of committees from each

case:

\mathrm{ 80+90+1=171 . }

Therefore, there are 171 different committees that can be formed where at least 3 women must be on the committee.

Posted by

Gaurav

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2026 final key soon; objection window closes today
anam-khan

100 marks in JEE Mains 2026 Percentile: Know rank trends, admission chances at NITs, IIITs
anam-khan

NIT vs GFTI: Which requires a lower JEE Main cutoff?

Latest Question