Question

in how many ways can 10boys and 10 girls sit together so that no 2 boys sit together​

Answer 1

Given

No 2 boys are not allowed to sit together. This means no boy is allowed to sit beside a boy.

This can be possible only when a boy is placed beside a girl.

First arrangle girls:

10 girls can be arranged in 10! ways.

Now place the boys in between girls so that no two boys will be together.

_ G₁ _G₂ _G₃ _G₄ _G₅ _G₆ _G₇ _G₈ _G₉ _ G₁₀ _

It is clear that in between 10 girls, there are 11 gaps.

In these 11 gaps select any 10 gaps and place the boys in that 10 gaps.

10 gaps can be selected from 11 gaps in ¹¹C₁₀ ways. = 11 ways

Again, in that selected 10 gaps 10 boys can be arranged in 10! ways.

Finally, number of ways of placing 10 boys and 10 girls so that no 2 boys sit together is = 11 * 10! * 10! ways.

Answer is 11*10!*10! ways.

Hope, this helps you.