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  • A committee of 6 people needs to be formed from a group of 12 individuals, including 5 men and 7 women. If the committee must have an equal number of men and women, how m

A committee of 6 people needs to be formed from a group of 12 individuals, including 5 men and 7 women. If the committee must have an equal number of men and women, how many different committees can be formed?

 

Option: 1

225


Option: 2

350


Option: 3

450


Option: 4

335


Answers (1)

best_answer

To calculate the number of different committees that can be formed with an equal number of men and women, we can consider different scenarios based on the number of men and women on the committee.

Since we need an equal number of men and women, we can choose 3 men and 3 women from the available individuals.

The number of ways to select 3 men from 5 men is given by \mathrm{C(5,3)=10.}

The number of ways to select 3 women from 7 women is given by \mathrm{C(7,3)=35.}

To find the total number of committees that satisfy the given condition, we multiply the number of possibilities for men and women:

\mathrm{ 10 \times 35=350 . }

Therefore, there are 350 different committees that can be formed with an equal number of men and women.

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SANGALDEEP SINGH

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