Ans: E
After not being actively engaged in a large overseas conflict for several years,
1969 saw the instatement of a draft lottery for those born between 1944 and 1950 in the United States and thus eligible for military service.
starting modifier seems to be modifying year 1969, but that does not make meaning clear. something was not engaged in conflict for several years - only C or E present some subjects which can be associated with opening modifier
Between C and E US makes more sense, as modifier is taking about overseas conflict.
A) 1969 saw the instatement of a draft lottery for those born between 1944 and 1950 in the United States and thus eligible
B) the United States’ instatement of a draft lottery in 1969 made those born between the time of 1944 and 1950 eligible
C) a draft lottery was instated in 1969 for those born between 1944 and 1950 in the United States, making them eligible
D) the year 1969 saw the instatement of a draft lottery, making eligible those born in the United States between 1944 and 1950
E) the United States in 1969 instated a draft lottery for those born between 1944 and 1950 and thus made them eligible