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  • In a group of 14 students, how many different ways can you select a team of 3 students to participate in a quiz if at least 2 of them must be from a specific grade?  <div class='qna

In a group of 14 students, how many different ways can you select a team of 3 students to participate in a quiz if at least 2 of them must be from a specific grade?
 

Option: 1

19


Option: 2

18


Option: 3

10


Option: 4

13


Answers (1)

best_answer

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 frorn the remaining 14-2=12 students (excluding the 2 from the specific grade).

Number of ways to select 1 student from 12=12 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 possiblities from both cases:

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

Total number of ways =12 C1+1

Now, let's calculate the value:

Total number of ways =12+1=13

Therefore, there are 13 different ways to select a team of 3 students to participate in the quiz, where at least 2 of them must be from a specific grade.

Posted by

Anam Khan

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