Verified Solution • 2025–26 Session moderate

QJEEM23Ma12ad: JEE Main 2023 Mathematics - Class 11 JEEM23Ma12ad Solution: The number of ways, in which 5 girls and 7 boys can be seated…

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is :

Multiple Choice Options

  • A 720
  • B 7(360)27(360)^{2}
  • C 7(720)27(720)^{2}
  • D 126(5!)2126(5 !)^{2}

Step-by-Step Verified Solution

We have,

Number of girls =5=5

Number of boys =7=7

JEE Main 2023 (Online) 8th April Morning Shift Mathematics - Permutations and Combinations Question 39 English Explanation

So, number of ways of arranging boys

around the table =6=6 ! and 5 girls can be arranged in 7 gaps in 7P5{ }^7 \mathrm{P}_5 ways.

∴\therefore Required no. of ways =6!×7P5=6 ! \times{ }^7 \mathrm{P}_5 =126×(5!)2=126 \times(5 !)^2

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring