Independent solution

How to solve this Inclusion–Exclusion question

Setup

Setup

Within the young group Y, the requested cell excludes both the male group M and the married group R.

N(Y∩F∩S)=N(Y)−N(Y∩M)−N(Y∩R)+N(Y∩M∩R)N(Y\cap F\cap S)=N(Y)-N(Y\cap M)-N(Y\cap R)+N(Y\cap M\cap R)

Model

Model

Subtract the two excluded groups from N(Y). Their overlap is removed twice by that subtraction, so add the young, male, married cell back once.

N(Y∩F∩S)=3000−1320−1400+600N(Y\cap F\cap S)=3000-1320-1400+600

Compute

Compute

Substitution gives 3000-1320-1400+600=880 records in the requested cell.

N(Y∩F∩S)=880N(Y\cap F\cap S)=880

Answer

Answer

Therefore the required count is 880, corresponding to choice D.

880(D)\boxed{880\quad\text{(D)}}