Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • There are 10 students in a classroom and 10 chairs for them to sit on. The instructor makes them sit in a different spot each month. How many times can the instructor force them to sit in

There are 10 students in a classroom and 10 chairs for them to sit on. The instructor makes them sit in a different spot each month. How many times can the instructor force them to sit in class?

Option: 1

9!


Option: 2

8!


Option: 3

10!

 


Option: 4

11!


Answers (1)

best_answer

Given that,

There are 10 available chairs for 10 children to sit in.

Thus, their instructor will use the fundamental counting principle to determine the number of ways she can make them sit.

In the first month, there are 10 students available to sit on any of the 10 chairs. So, the number of possible arrangements in the first month is 10!.

In the second month, since the instructor wants the students to sit in a different spot, each student can sit in any of the remaining 9 chairs. So, the number of possible arrangements in the second month is 9!.

Following the same logic, for each subsequent month, the number of possible arrangements decreases by 1.

To find the total number of times the instructor can force them to sit in a different spot, we need to calculate the product of the arrangements for each month.

Thus, the number of arrangements is given by,

10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2=10!

Therefore, the number of ways the teacher makes seating arrangements is 10! ways.

 

Posted by

Nehul

View full answer

JEE Main high-scoring chapters and topics

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

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025: Previous year NIT Calicut cut offs; opening, closing ranks
anam-khan

JEE Main 2025 Admit Card Live: Session 1 hall ticket soon at jeemain.nta.nic.in; photo correction, cut-offs
anam-khan

NTA finds errors in JEE Main 2025 photos; asks to upload correct images by January 17

Latest Question