Question

Twenty persons are invited for a party. In how many different ways can the host be seated at a circular table, if two particular persons are to be seated on either side of the host?

Answer 1

@kropot72

Answer 2

two persons so 2!

Answer 3

do you know permutation....?

Answer 4

@dg2

Answer 5

somewhat!blindly without proper concept

Answer 6

@paki i hav lost the connection

Answer 7

19 ways twenty persons seated,then two persons on either side so 2!

Answer 8

18!*2 ways i know the answer but it is not clear to me

Answer 9

what is the total number of people...?

Answer 10

20

Answer 11

I don't understand where there are only 18!*2 ways either. Are you sure you didn't mean 18!*20?

Answer 12

where=why

Answer 13

yes

Answer 14

Wait, just realized I made a mistake. Let me reconsider.

Answer 15

First, is the host included among those 20 people invited?

Answer 16

20 persons so 19 ways

Answer 17

Okay, assuming the host is one of the 20 people. Here's my formulation.

First, of the 20 seats, choose 1 for the host. Next, he has two seats next to him. For the 2 people that are suppose to sit next to him, there are 2 ways to seat them. Now, we have 17 remaining people, and they can be in any arrangement in the remaining chairs.

20*2*17!

Answer 18

After fixing the places of three persons (1 host + 2 persons) and treating them as 1 unit we can arrange the total (20 - 2 + 1) = 19 units in 18! ways. Again these particular persons can sit on either side of the host in 2 ways.

Hence the total number of ways is 18! × 2

Answer 19

First, you are not counting the host as 1 of the 20?

Answer 20

then

Answer 21

Then what? I'm just trying to figure out if you're including the host as one of the twenty. :)

Answer 22

see 20 people seated in how many ways

Answer 23

Okay, since I assume this means we are to count the host as one of the twenty people, my earlier formation would seem correct:

20 ways to seat the host, 2 ways to seat the people who are suppose to sit next to him, and 17! ways to seat the rest. So, 20*2*17! = 30*17!

Answer 24

nope .18!*2 is the answer

Answer 25

How do you think they arrived at 18!*2?

Answer 26

First, it seems I was solving the wrong problem. I was solving the problem: How many ways can people be seated at the circular table, given that the host will have two particular people of those 19 non-hosts who must sit next to him.

Answer 27

After fixing the places of three persons (1 host + 2 persons) and treating them as 1 unit we can arrange the total (20 - 2 + 1) = 19 units in 18! ways. Again these particular persons can sit on either side of the host in 2 ways. Hence the total number of ways is 18! × 2

Answer 28

Oh well, I don't think I understand what the question is actually asking. The answer makes no sense to me.