Question

A company has 10 software engineers and 6 civil engineers. In how many ways can they be seated around a round table so that all the civil engineers are together

Answer 1

There are 10 software engineers and 6 civil engineers.

We will consider the group of 6 civil engineers as single civil engineer, because they are together.

So for 10 software engineer and one civil engineer :  n = 11.

They can be arranged around the table in ( n- 1 ) !  ways.

( 11 - 1 ) ! = 10 !

Also civil engineers can be arranged among themselves as 6 !  ( permutations with n = 6 )

Finally:  10! * 6!

Answer: They can be seated around a round table in 10! * 6! ways.