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  • Determine the number of ways to form a committee of 9 members from a group consisting of 8 boys and 4 girls, with the condition that at least one boy must be included  <div class

Determine the number of ways to form a committee of 9 members from a group consisting of 8 boys and 4 girls, with the condition that at least one boy must be included

 

Option: 1

320


Option: 2

220


Option: 3

640


Option: 4

820


Answers (1)

best_answer

To determine the number of ways to form a committee of 9 members from a group of 8 boys and 4 girls, with the condition that at least one boy must be included, we can use the principle of inclusion-exclusion.

First, we calculate the total number of ways to form a committee of 9 members from the total group of 12 students (8 boys + 4 girls). This can be calculated using the combination formula:

\mathrm{C(12,9)=12 ! /(9 ! \times(12-9) !)=220}

Next, we calculate the number of ways to form a committee of 9 members from the group of girls only, which is:

\mathrm{C(4,9)=4 ! /(9 ! \times(4-9) !)=0}

(since there are not enough girls to form a committee of 9)

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

220 - 0 = 220

Therefore, there are 220 ways to form a committee of 9 members from a group consisting of 8 boys and 4 girls, with the condition that at least one boy must be included.


 

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Gaurav

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