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  • A committee of 5 people needs to be selected from a group of 10 individuals, including 4 men and 6 women. If at least 2 women must be on the committee, how many different

A committee of 5 people needs to be selected from a group of 10 individuals, including 4 men and 6 women. If at least 2 women must be on the committee, how many different committees can be formed?

 

Option: 1

246

 


Option: 2

320

 


Option: 3

140

 


Option: 4

260


Answers (1)

best_answer

To calculate the number of different committees that can be formed, where at least 2 women must be on the committee, we can consider different scenarios based on the number of women on the committee.

Case 1: Selecting 2 women and 3 men:

The number of ways to select 2 women from 6 women is given by \mathrm{C(6,2)=15.}

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{15 \times 4=60.}

Case 2: Selecting 3 women and 2 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 2 men from 4 men is given by \mathrm{C(4,2)=6.}

The total number of committees in this case is \mathrm{20 \times 6=120}

Case 3: Selecting 4 women and 1 man:

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 1 man from 4 men is given by \mathrm{C(4,1)=4}

The total number of committees in this case is \mathrm{ 15 \times 4=60.}

Case 4: Selecting 5 women:

The number of ways to select 5 women from 6 women is given by \mathrm{ C(6,5)=6.}

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

case:

\mathrm{ 60+120+60+6=246 . }

Therefore, there are 246 different committees that can be formed, where at least 2 women must be on the committee.

Posted by

Deependra Verma

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