At Information and Communications University: 31 female seniors were on the dean's list 62 women were on the dean's list who were not seniors 45 male seniors were on the dean's list 87 female seniors were not on the dean's list 96 male seniors were not on the dean's list 275 women were not senior and were not on the dean's list 88 men were on the dean's list who were not seniors 227 men were not seniors and were not on the dean's list (a) How many were seniors? (b) How many were women? (c) How many were on the dean's list? (d) How many were seniors on the dean's list? (e) How many were female seniors? (f) How many were women on the dean's lists? (g) How many were students at the college?

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