Answer to Question #279373 in Discrete Mathematics for Jaishree

Question

In a survey on the gelato preferences of college students, the following data was

obtained: • 78 like mixed berry • 32 like irish cream • 57 like tiramisu • 13 like

both mixed berry and irish cream • 21 like both irish cream and tiramisu • 16

like both tiramisu and mixed berry • 5 like all three flavours above • 14 like none

of these three flavours How many students were surveyed?

Answer 1

$$N(B\cup C\cup T)=N(B)+N(C)+N(T)$$

$$-N(B\cap C)-N(B\cap T)-N(C\cap T)$$

$$+N(B\cap C\cap T)$$

$$=78+32+57-13-21-16+5$$

$$=122$$

$$N(U)=N(B\cup C\cup T)+N((B\cup C\cup T)^C)$$

$$=122+14=136$$

136 students were surveyed.