Question Number 114797 by bemath last updated on 21/Sep/20

There are 6 people going to sit in   a circle . The number of arrangements  they sit if there are 2 people who  always sit next to each other

Answered by mr W last updated on 21/Sep/20

2×4!=48

Commented bybemath last updated on 21/Sep/20

gave kudos

Commented bybemath last updated on 21/Sep/20

sir why not C_2 ^6 ×2×4! sir

Commented bymr W last updated on 21/Sep/20

we have always two people next to  each other. here it is meant that two  particular people are next to each  other, so you can not select two any  people from 6.

Commented bybemath last updated on 21/Sep/20

the conditions under which the   C_2 ^6  is taken into account sir

Commented bymr W last updated on 21/Sep/20

if the question is:  there are 10 seats on a round table.  in how many ways can 6 people sit  on the table such that at least two  people are next to each other?

Commented bybemath last updated on 21/Sep/20

for this question the answer is   C_2 ^6 ×2×C_6 ^(10) ×4! sir

Commented bymr W last updated on 21/Sep/20

C_2 ^6 ×2×C_4 ^8 ×4!  or  C_2 ^6 ×2×P_4 ^8