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- In a group of 11 students, how many different ways can you select a team of 3 students to participate in a quiz if exactly 2 of them must be from a specific grade? <div class='qna-
In a group of 11 students, how many different ways can you select a team of 3 students to participate in a quiz if exactly 2 of them must be from a specific grade?
13
51
10
12
Answers (1)
To solve this problem, we'll consider two cases: when exactly 2 students are chosen from the specific grade and when all 3 students are chosen from the specific grade.
Case 1: Exactly 2 students from the specific grade are chosen.
In this case, we need to select the remaining 1 student from the remaining 11-2=9 students (excluding the 2 from the specific grade).
Number of ways to select 1 student from 9=9 C1
Case 2: All 3 students from the specific grade are chosen.
There is only 1 way to select all 3 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
Total number of ways =9 C1+1
Now, let's calculate the value:
Total number of ways =9+1=10
Therefore, there are 10 different ways to select a team of 3 students to participate in the quiz, where exactly 2 of them must be from a specific grade.
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