Question

In how many distinct ways can nine (9) people be seated in a row if four (4) of the people are in a polyamorous relationship and must be grouped together?

Answer 1

We've given 9 peoples in which 4 of them are always together and remember all of the 9 peoples are not same

Now we consider those 4 persons who are always together as 1 unit

[1st 2nd 3rd 4th] 5th 6th 7th 8th 9th

So we have 6 things or 6 people to be arranged

`6!=720`

BUT

Inside only we know there is a group of 4 people who can also interchange their positions

`6!\cdot4!\text{ =}17280`

Hence our final answer will be 17280