Question

a survey of 600 students yielded the following information: 159 were seniors, 378 were commuters, and 88 were seniors and commuters. how many students were neither seniors nor commuters?

Explanation:

Step1: Use inclusion - exclusion principle

$n(S\cup C)=n(S)+n(C)-n(S\cap C)$
where $n(S) = 159$, $n(C)=378$, $n(S\cap C)=88$.
So $n(S\cup C)=159 + 378-88=449$.

Step2: Find non - S and non - C

Total students $N = 600$.
Students neither seniors nor commuters $=600 - n(S\cup C)=600 - 449 = 151$.

Answer:

151