Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a cir-
cular table. In how many ways can they be seated so that no two persons whose badges have
consecutive numbers are seated next to each other? (Two arrangements obtained by rotation
around the table are considered different.)
Answers
Answer:
10
Step-by-step explanation:
Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a circular table
Lets number position
A , B , C , D , E in circle
so now fix badge with number 1 at position A
ABCDE is in circle
=> E & B are next to A
=> badge number 2 Can seat at C or D
if 2 Sits at C
then B & D are next
=> 3 has to Sit on E (as A & C are already occupied)
D is next to E
=> 4 has to sit on B
& 5 has to sit on D
if 2 Sits at D
then C & E are next
=> 3 has to Sit on B (as A & D are already occupied)
C is next to B
=> 4 has to sit on E
& 5 has to sit on C
=> if 1 sits on A then 2 arrangements are possible
now its given that
Two arrangements obtained by rotation around the table are considered different.
=> 1 can sit on B , C , D , E also
=> Total Arrangements = 2 * 5 = 10
60 Possible Ways!
Step-by-step explanation:
All things considered, there are 5!=120 approaches to sort out people if every one of them could sit on each seat. Presently, we should perceive what number of changes there are for the situation that the individual A sits on seat 3: 4x3x1x2x1=24
How about we start with individual D who is the most prohibitive. We will think about 2 cases:
D sits in seat 2 or 4
D sits in seat 3
In the event that D sits in seat 2 or 4, next, we take a gander at individual A who can't sit in seat 3. There are just 3 seats accessible to A. At that point 3 to B, 2 to C, and 1 to E. That is: 2x3x3x2x1=36
On the off chance that D sits in seat 3, at that point, there are 4!=24 approaches to mastermind the rest of the individuals, as there are no more limitations.
That is a sum of 36+24=60.