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  • In a group of 13 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?<di

In a group of 13 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

652


Option: 2

132


Option: 3

252


Option: 4

322


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 the other 2 students are chosen from the remaining grades.

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 13 - 1 = 12 students (excluding the 1 from the specific grade).

Number of ways to select 2 students from 12=12\mathrm{C}2

Case 2: The other 2 students are chosen from the remaining grades.

In this case, we need to select 2 students from the remaining 13 - 1 = 12 students (excluding the 1 from the specific grade).

Number of ways to select 2 students from 12=12\mathrm{C}2

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 =12C2+12C2}}

Now, let's calculate the value:

\mathrm{\text{Total number of ways =66+66=132}}

Therefore, there are 132 different ways to select a team of 3 students to participate in the quiz, where exactly 1 of them must be from a specific grade.

Hence option 2 is correct.

 

Posted by

Gautam harsolia

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