I have to arrange 5 people around a rectangular table, but Max and Suzie must sit together. How many ways do I have of arranging these crazy people?
Though Max and Suzie must seat together,then they should be treated as one unit.then the arrangements will be of 4!=4*3*2*1=24.these arrangements have two sets-first, on the left Max and second,on the left Suzie.hence the total arrangements will be of 24*2=48.
this is an example of circular permutation bcz the persons are to be sit in a circle around a table.
we will first assume that max and suzie are only 1 person. (Do jism ek jaan). so we are left with only 4 persons.
in circular permutation, total number of ways are (n-1)! so in this case, (4-1)!= 3!
now max and suzie can sit in 2! ways themselves.
so total number of ways are- 2!*3!