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  • In a group of 10 students, how many different ways can you select a team of 3 students to participate in a quiz if exactly 1 of them must be from a specific grade?<stron

In a group of 10 students, how many different ways can you select a team of 3 students to participate in a quiz if exactly 1 of them must be from a specific grade?

Option: 1

44


Option: 2

84


Option: 3

10


Option: 4

60


Answers (1)

best_answer

To solve this problem, we'll consider two cases: when exactly 1 student is chosen from the specific grade and when 2 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 2 students from the remaining 10-1=9 students (excluding the 1 from the specific grade).

Number of ways to select 2 students from 9=9 C2

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

In this case, we need to select 1 more student from the specific grade and 1 student from the remaining 10-2=8 students.

Number of ways to select 1 student from the specific grade = 1 (since there is only 1 student from the specific grade)

Number of ways to select 1 student from 8=8 C 1

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 C2+1 \times 8 C1

Now, let's calculate the value:

Total number of ways =36+1 \times 8=44

Therefore, there are 44 different ways to select a team of 3 students to particlpate in the quiz, where exactly 1 of them must be from a specific grade.

Posted by

Ajit Kumar Dubey

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