Question

If 2 boys and 2 girls are to be arranged in a row so that the girls are not next to each other, how many possible arrangements are there?

Answer 1

together 2 all the boys can sit and in 3 girls cannot be possible

Answer 2

The no. of possible arrangements is 12.

Solution:  

The arrangement of “2 boys and 2 girls” is in 4! Ways=

= $4 \times 3 \times 2 \times 1$ = 24 ways

Now, 2 girls can be together in 3! ways=

=$3 \times 2 \times 1$ =6 ways

In the condition of girls are together they can change their seats among themselves in 2! ways =$2 \times 1$ = 2

Therefore, no of ways in which both the girls will not be together =4 !-$(3 ! \times 2 !)$

=24-$(6 \times 2)$

=24-12

=12

Hence number of possible arrangements is 12.