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  • A group of 5 students, including 3 boys and 2 girls, is going to sit in a row for a photo. If the boys and girls must alternate seats, in how many different ways can they

A group of 5 students, including 3 boys and 2 girls, is going to sit in a row for a photo. If the boys and girls must alternate seats, in how many different ways can they be arranged?

 

Option: 1

12


Option: 2

15


Option: 3

10


Option: 4

20


Answers (1)

best_answer

To calculate the number of different ways the group of 5 students can be arranged in a row, with the boys and girls alternating seats, we can treat the boys and girls as separate entities.

Since there are 3 boys and 2 girls, we have the following pattern: BGBGB.

Now, let's consider the number of ways to arrange the boys within themselves and the girls within themselves.

The number of ways to arrange the boys among themselves is given by 3 !, and the number of ways to arrange the girls among themselves is given by 2 !.

Therefore, the total number of different ways to arrange the group of students with the boys and girls alternating seats is:

\mathrm{ 3 ! \times 2 !=6 \times 2=12 . }

Therefore, there are 12 different ways the group of 5 students can be arranged in a row, with the boys and girls alternating seats.

Posted by

avinash.dongre

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