Question

5. Five persons wearing badges with numbers 1,2,3,4,5 are seated on 5 chairs around a
cular table. In how many ways can they be seated so that no two persons whose badges nav
consecutive numbers are seated next to each other? (Two arrangements obtained by rotation
around the table are considered different.)​

Answer 1

Answer:

10 arrangements

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

10 arrangements