Since the order of the selected essays is not important, we need to find the number of different three elements subsets of a set with 4 elements (the number of 3-combinations of 4 elements):

C(4, 3) = 4!/((4 - 3)!*3!) 

C(4, 3) = 4

Another way to solve this is to denote the essays with A, B, C and D, write down and count all the possible subsets with 3 elements from the set {A, B, C, D}:

{A, B, C}

{A, B, D}

{B, C, D}

{A, C, D}

Indeed, there are 4 different subsets with 3 elements.