JEE Main Mathematics Question (2026) — Solution

Step-by-step solution

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