Total number of boys =4
Total number of girls =3
Total number of children =7
Total number of ways to arrange 7 children in a queue =7!=5040
To find the number of ways where all 3 girls are together, consider the 3 girls as a single unit.
Total number of units to arrange =4 boys +1 unit of girls =5 units.
Number of ways to arrange these 5 units =5!=120
Number of ways to arrange the 3 girls among themselves =3!=6
Total number of ways where all girls are together =5!×3!=120×6=720
Number of ways such that all the girls are not together =Total ways−Ways where all girls are together
=5040−720=4320
Answer: 4320