Step-by-step explanation:
There's a lot of information here, so first things first, let's get organized.
Let's start by assigning variable names to each group. We want the variables to be short but easy to understand.
For example, let's say the number of female seniors on the dean's list is FSD (F for female, S for senior, and D for dean's list).
FSD = 31
Sticking to this naming scheme:
FD = 62
MSD = 45
FS = 87
MS = 96
F = 275
MD = 88
M = 227
Now we can begin.
a) We want to know how many seniors there are. So all we have to do is add up all the variables with an S in them.
FSD + MSD + FS + MS
31 + 45 + 87 + 96
259
b) We want to know how many women there are. So add up all the variables with an F in them.
FSD + FD + FS + F
31 + 62 + 87 + 275
455
c) We want to know how many are on the dean's list. So add up all the variables with a D in them.
FSD + FD + MSD + MD
31 + 62 + 45 + 88
226
d) Now we want to know how many are seniors AND on the dean's list. So add up all the variables that have both an S and a D.
FSD + MSD
31 + 45
76
e) We want to know how many female seniors there are, so add up all the variables with both an F and an S.
FSD + FS
31 + 87
118
f) We want to know how many women were on the dean's list, so add up all the variables with both an F and a D.
FSD + FD
31 + 62
93
g) Finally, we want to know how many students there are total. So add up all the variables.
FSD + FD + MSD + FS + MS + F + MD + M
62 + 45 + 87 + 96 + 275 + 88 + 227
880
