Hello I need someone to help me with work. English is my second language. I'm having hard time understanding it.
Among the $40$ campers at Camp Forlorn one week, $14$ fell into the lake during the week, $13$ suffered from poison ivy, and $16$ got lost trying to find the dining hall. Three of these campers had poison ivy rash and fell into the lake, $5$ fell into the lake and got lost, $8$ had poison ivy and got lost, and $2$ experienced all three misfortunes.
A) How many campers got through the week without any of these mishaps?
B) How many campers suffered from poison ivy only (did not had any other mishap)?
C) How many campers fell into the lake and got lost trying to find the dining hall, but did not get poison ivy?
D) How many campers fell into the lake and/or suffered from poison ivy?
Let A denote the number of people who fell into the lake, B denote the number of people who suffered from poison ivy, C denote the number of people who got lost.
From the information given,
$n(A)=14 \\ n(B)=13 \\ n(C)=16 \\ n(A \cap B)=3 \\ n(A \cap C)=5 \\ n(B \cap C) = 8 \\ n(A \cap B \cap C)=2$
Working backwards,
Those in the set $A\cap B$ only has $3-2=1$ people, those in the set $A \cap C$ only has $5-3=2$ people, those in the set $B \cap C$ only has $8-2=6$ people.
Those in the set $A$ only has $14-1-2-2=9$ people, those in the set $B$ only has $13-1-6-2=4$ people, those in the set C only has $16-2-6-2=6$ people.
Hence to find those without any misshaps, $40-1-2-6-9-4-6-2=10$