Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • For a photo, 7 children must be seated in a row on 7 chairs. Out of these, 4 are girls and the rest are boys. Find out all the ways that the 4 girl children are together.<div class='q

For a photo, 7 children must be seated in a row on 7 chairs. Out of these, 4 are girls and the rest are boys. Find out all the ways that the 4 girl children are together.

Option: 1

3465


Option: 2

4464


Option: 3

3672

 


Option: 4

5364


Answers (1)

best_answer

Given that,

There are 7 children who must be seated in a row on 7 chairs.

Therefore, if we find the number of ways in which all 4 girls occupy consecutive seats and subtract this number from the total number of ways in which the 7 children can be arranged among themselves, we will get the required answer.

7 children can be arranged among themselves in ^{7}P_7  ways

Thus,

^{7}P_7=5040

Assume that the 4 girls are one entity. The total number of ways in which they can be arranged among themselves is 4! Ways.

Also, the set of 4 girls and the other children can be arranged among themselves in 4! ways.

Thus, the total number of ways in which three girls are together is given by,

4!\times4!=576

Thus, the number of ways in which all 4 girls will not occupy consecutive seats is given by,


5040-576=4464

Therefore, the total number of ways to arrange the children for a photograph is 4464.

 

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

Trending Articles/News

anam-khan

JEE Main 2025: NIT Rourkela cut-offs for CSE, chemical engineering drop; last years' closing ranks
anam-khan

JEE Main 2025 Live: NTA exam city slip at jeemain.nta.nic.in soon; session 1 schedule
anam-khan

JEE Main 2025 schedule out for session 1; paper 1 from January 22

Latest Question