Q: In this task, you need to answer the given multiple-choice question on geometry. Classify your answers into 'a', 'b', 'c', 'd', and 'e'.
Problem: amit and ian paint a wall in alternating shifts . first amit paints alone , then ian paints alone , then amit paints alone , etc . during each of his shifts , amit paints 1 / 2 of the remaining unpainted area of the wall , while ian paints 1 / 3 of the remaining unpainted area of the wall during each of his shifts . if amit goes first , what fraction of the wall ' s area will remain unpainted after amit has completed his 6 th shift ?
Options: ['a ) 1 / 27', 'b ) 1 / 54', 'c ) 1 / 81', 'd ) 1 / 162', 'e ) 1 / 486']
A:
e