Question

In how many distinct ways can $3$ ladies and $3$ gentlemen be seated at a round table, so that exactly any two ladies sit together?

Answer 1

REF.Image.

select 2 ladies from 3 ladies = ${}^3{C}_2$

= 3 ways

And they ladies can sit in 2 ways

Now considering 2 ladies as can

The remaining lady has only 2 seal left

she can occupy only 2 places.

There men can arrange themselves in 3!

so Total ways $=2{\times }^3{C}_2\times 2\times 6$

$=72$ ways