Sara has 6 flower pots, each having a unique flower. Pots are arranged in an arbitrary sequence in a row. Sara rearranges the sequence each day but not two pots should be arranged adjacent to each other which were already adjacent to each other in previous arrangement. How many days she can do this or how many such arrangements are possible ?
we have (62)=15 different pairs of pots. At each days Sara realizes 5 of these pairs as ajacent. Since all these pairs should be different, the number of days is at most 15/5=3 .
The following example describes the admissible list of arrangements for 3 days.