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  • A committee of 7 members is to be formed from a group of 8 boys and 4 girls. In how many ways can the committee be formed if at least one girl must be included?  <div class='qna-

A committee of 7 members is to be formed from a group of 8 boys and 4 girls. In how many ways can the committee be formed if at least one girl must be included?

 

Option: 1

784


Option: 2

660


Option: 3

485


Option: 4

820


Answers (1)

best_answer

To calculate the number of ways the committee can be formed from a group of 8 boys and 4 girls, with at least one girl included, we can use the principle of inclusion-exclusion.

First, we calculate the total number of ways to form a committee of 7 members from the total group of 12 students (8 boys + 4 girls). This can be calculated using the combination formula:

\mathrm{C(12,7)=12 ! /(7 ! \times(12-7) !)=792}

Next, we calculate the number of ways to form a committe only, which is:

\mathrm{C(8,7)=8 ! /(7 ! \times(8-7) !)=8}

Since we want to include at least one girl in the committee, we subtract the number of committees consisting only of boys from the total number of committees:

792 - 8 = 784

Therefore, there are 784 ways to form a committee of 7 members from a group of 8 boys and 4 girls, where at least one girl must be included.

 

Posted by

Gautam harsolia

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