Combinatorics: How many persons like apples and pears and strawberries? Out of $32$ persons, every person likes to eat at least one of the following type of fruits: Strawberries, Apples and Pears. (Which means that there does not exist any person, who does not like to eat any type of fruit). Furthermore, we know that $20$ persons like to eat apples, $18$ persons like to eat pears and $28$ persons like to eat strawberries.
(a) There are $10$ persons who like apples and pears, $16$ persons who like apples and strawberries, and $12$ persons who like pears and strawberries.
How can I find out how many people like apples as well as pears as well as strawberries?
To structure this a bit:


*

*$32$ persons

*$20 \rightarrow$ apples ($\rightarrow$ meaning "like")

*$18 \rightarrow$ pears

*$28 \rightarrow $ strawberries


And for (a)


*

*$10$ persons $\rightarrow$ (apples & pears)

*$16$ persons $\rightarrow$ (apples  & strawberries)

*$12$ persons $\rightarrow$ (pears & strawberries)


Since we know that the total number of persons is $32$. 
Can I just do the following? 
Because $20$ persons like apples I can just add the following numbers together: 
$10 \rightarrow$ ($10$ apples & $0$ pears) + $16 \rightarrow$ ($6$ apples & $10$ strawberries) $+ 12 \rightarrow$ ($12$ pears & $0$ strawberries). So in total I'd get $10 + 16 + 12 = 28$ people who like apples, pears and strawberries? Is that correct? 
(b) Assume that you don't have the information in (a). Give the preferably  limits for the amount of persons who like to eat all kind of fruits.
Since $18$ person like pears, can I just say that $18$ persons like to eat pears, apples and strawberries? (As $18$ is the minimal amount of fruits).

What you have actually worked out for part a) is the number of people who don't like all three. So since there are $32$ people, and $28$ don't like all three, the number of people who like Apples, Pears and Strawberries is $4$.
