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In a group of 9 students, how many different ways can you select a team of 2 students to participate in a quiz if at least 1 of them must be from a specific grade?

 

Option: 1

6


Option: 2

8


Option: 3

9


Option: 4

1


Answers (1)

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To solve this problem, we'll consider two cases: when exactly 1 student is chosen from the specific grade and when both students are chosen from the specific grade.

Case 1: Exactly 1 student from the specific grade is chosen.

In this case, we need to select the remaining 1 student from the remaining 9 - 1 = 8 students (excluding the 1 from the specific grade).

Number of ways to select 1 student from8=8\mathrm{C}1

Case 2: Both students are chosen from the specific grade.

There is only 1 way to select both students from the specific grade.

To calculate the total number of ways to form the team, we need to sum up the possibilities from both cases:

Total number of ways = Number of ways in Case 1 + Number of ways in Case 2

\mathrm{\text{Total number of ways = 8C1+1}}

Now, let's calculate the value:

\mathrm{\text{Total number of ways = 8 + 1 = 9}}

Therefore, there are 9 different ways to select a team of 2 students to participate in the quiz, where at least 1 of them must be from a specific grade.

Hence option 3 is correct.

Posted by

Irshad Anwar

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