5 boys and 6 girls are arranged in all possible ways. Let X denote the number of linear arrangements in which no two boys sit together and Y denote the number of linear arrangements in which no two girls sit together. If Z denote the number of ways of arranging all of them around a circular table such that no two boys sit together, then X: Y: Z=

Step-by-step solution

When no two boys sit together, * G * G * G * G * G * G * X= Number of ways of arrangement in which no two boys sit together = ^7 C₅ 5! 6! When no two girls sit together ^* ~B * ~B * ~B * ~B * ~B * Y= Number of ways of arrangement in which no two girls sit together = ^6 C₆ 5! 6 ! If Z= Number of ways of arranging all of them around a circular toable such that no two boys sit together aligned & = ^6 C₅ 5! 5! & X: Y: Z= ^7 C₅ 5! 6! ^6 C₆ 5! 6! ^6 C₅ 5! 5! & =21: 1: 1 aligned