Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • In a group of 15 students, how many different ways can you select a team of 4 students to participate in a quiz if exactly 1 of them must be from a specific grade?

In a group of 15 students, how many different ways can you select a team of 4 students to participate in a quiz if exactly 1 of them must be from a specific grade?

 

Option: 1

962


Option: 2

728


Option: 3

620

 


Option: 4

350


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 3 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 3 students from the remaining 15 - 1 = 14 students (excluding the 1 from the specific grade).

Number of ways to select 3 students from 14=14\mathrm{C}3

Case 2: The other 3 students are chosen from the remaining grades.

In this case, we need to select 3 students from the remaining 15 - 1 = 14 students (excluding the 1 from the specific grade).

Number of ways to select 3 students from :14=14\mathrm{C}3

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

\mathrm{\text{Total number of ways = Number of ways in Case 1 + Number of ways in Case 2}}

\mathrm{\text{Total number of ways = 14C3+14C3}}

Now, let's calculate the value:

\mathrm{\text{Total number of ways =364 + 364 = 728}}

Therefore, there are 728 different ways to select a team of 4 students to participate in the quiz, where exactly 1 of them must be from a specific grade.

Hence option 2 is correct.

 

Posted by

Ajit Kumar Dubey

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Latest Question