If $11$ members of a committee sit around at a round table so that the president and secretary always sit together, then the number of arrangements, is 

Given :  $11$ members of a committee sit around at a round table so that the president and secretary always sit together
To find : number of arrangements. 

A permutation is a (possible) rearrangement of objects 

By using formula $n! = 1.2. 3 ....(n-1) . n$

Since, out of $11$ members, $2$ members sit together then the number of arrangements $= 9! \times 2$

( $\because 2$ members can sit in $2$ ways )