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  • A classroom has 30 students, including 10 boys and 20 girls. If a committee of 6 students needs to be formed, in how many different ways can the committee be formed if th

A classroom has 30 students, including 10 boys and 20 girls. If a committee of 6 students needs to be formed, in how many different ways can the committee be formed if there must be an equal number of boys and girls?

 

Option: 1

125,000

 


Option: 2

136,800

 


Option: 3

142,200

 


Option: 4

186,600


Answers (1)

best_answer

To calculate the number of different ways a committee of 6 students can be formed from a classroom of 30 students, with an equal number of boys and girls in the committee, we need to consider the available options for each gender.

Since there are 10 boys and 20 girls, we need to select 3 boys and 3 girls to form the committee.

The number of ways to select 3 boys from 10 boys is given by \mathrm{C(10,3)=120}

The number of ways to select 3 girls from 20 girls is given by \mathrm{ C(20,3)=1140 }

To find the total number of different committees that satisfy the given condition, we multiply the number of possibilities for boys and girls:

\mathrm{ 120 \times 1140=136,800 . }

Therefore, there are 136,800 different ways the committee of 6 students can be formed, with an equal number of boys and girls.

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HARSH KANKARIA

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