Calculation:Let C, F and V denote the sets of number of students who play cricket, football and volleyball, respectively.? n(C) = 55, n(F) = 47 and n(V) = 42? n(C ? F) = 20, n(F ? V) = 22, n(C ? V) = 26? Let 'x' be the number of students who play all the 3 games.? Number of students who play both cricket and football, but not volleyball = (20 - x)? Similarly, number of students who play both football and volleyball, but not cricket = (22 - x)? Number of students who play both cricket and volleyball, but not football = (26 - x) ? Now, we can find the number of students who play cricket only, football only and volleyball only as follows:? n(C) only = 55 - (20 - x + x + 26 - x) = x + 9? Similarly for n(V) only = x + 5? And n(F) only = = x - 6 ? 84 = (x + 9) + (x + 5) + (x “ 6) + (20 - x) + (26 - x) + (22 - 4) + x? x = 8? Number of students who play only cricket = 8 + 9 = 17