Suppose a class contains 100 students. Let, for 1≤i≤100, the ith student have ai many friends. For 0≤j≤99 let us define cj to be the number of students who have strictly more than j friends. Show that \begin{align*} & \sum_{i=1}^{100}a_i=\sum_{j=0}^{99}c_j \end{align*} combinatorics proposedcombinatorics