Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • A group of 5 students, including 2 boys and 3 girls, is going to sit in a row for a photo. If the boys and girls must alternate seats, and the two boys cannot sit next to

A group of 5 students, including 2 boys and 3 girls, is going to sit in a row for a photo. If the boys and girls must alternate seats, and the two boys cannot sit next to each other, in how many different ways can they be arranged?

 

Option: 1

14


Option: 2

15


Option: 3

10


Option: 4

16


Answers (1)

best_answer

To calculate the number of different ways the group of 5 students can be arranged in a row for a photo, with the boys and girls alternating seats and the two boys not sitting next to each other, we can consider the following:

Since the boys and girls must alternate seats, we have the following pattern: BGBGB.

Now, let's consider the possible arrangements of the boys within this pattern.

Case 1: The boys sit in the first and third positions (BGBGB).

In this case, the remaining two girls can be arranged in 2 !=2 ways.

Case 2: The boys sit in the second and fourth positions (GBGBG).

In this case, the remaining two girls can also be arranged in 2 !=2 ways.

Therefore, there are 2+2=4 different arrangements for the boys and girls within the given pattern.

Hence, the total number of different ways the group of 5 students can be arranged is:

\mathrm{ 4 \times 2 ! \times 2 !=4 \times 2 \times 2=16 . }

Therefore, there are 16 different ways the group of 5 students can be arranged in a row for a photo, with the boys and girls alternating seats and the two boys not sitting next to each other.

Posted by

Divya Prakash Singh

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