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  • In how many ways can a committee of 3 boys and 2 girls be formed from a group of 7 boys and 5 girls?  Option: 1 64<div c

In how many ways can a committee of 3 boys and 2 girls be formed from a group of 7 boys and 5 girls?

 

Option: 1

64


Option: 2

42


Option: 3

44


Option: 4

48


Answers (1)

best_answer

To calculate the number of ways a committee of 3 boys and 2 girls can be formed, we need to choose 3 boys from a group of 7 boys and 2 girls from a group of 5 girls. We can use combinations to solve this problem.

The number of ways to choose 3 boys from 7 is denoted as \mathrm{C(7,3)},which can be calculated as:

\mathrm{C(7,3)=7 ! /(3 ! \times(7-3) !)=7 ! /(3 ! \times 4 !)=(7 \times 6 \times 5) /(3 \times 2 \times 1)=35}

Similarly, the number of ways to choose 2 girls from 5 is denoted as \mathrm{C(5,2)}, which can be calculated as:

\mathrm{C(5,2)=5 ! /(2 ! \times(5-2) !)=5 ! /(2 ! \times 3 !)=(5 \times 4) /(2 \times 1)=10}.

To find the total number of ways to form the committee of 3 boys and 2 girls, we multiply the number of ways to choose the boys and the number of ways to choose the girls:

Total ways \mathrm{=C(7,3) \times C(5,2)=35 \times 10=350}.

Therefore, there are 350 ways to form a committee of 3 boys and 2 girls from a group of 7 boys and 5 girls.

 

Posted by

Ritika Kankaria

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