Venn Diagram

Problem:
Three professors, X, Y, and Z of a department, are around for the position of Vice-Chancellor. Suppose 230 students are involved in the ranking overall. It was observed that 115 chose X, 112 chose Y, 131 chose Z. 56 chose Y and Z, Those who chose X and Z were two greater than X and Y. 19 students did not rank any. Find the number who rank;

(i) All the 3

(ii) only one

(iii) X and Z but not Y

See the excel file for the hint