Problem Solving

gmattesttaker2 wrote:Hello,

Can you please assist with this:

The subsets of set {s,u,t} are {s},{u},{t},{su},{st},{ut},{s,u,t},and the
empty set { }. How many of the subsets of set {s,u,t,w, x}do NOT contain element t?

(A) 13
(B) 14
(C) 15
(D) 15
(E) 16

This is very similar to this question: https://www.beatthegmat.com/combinatoric ... 73180.html


Here's one approach:

Take the task of building subsets and break it into stages.

Stage 1: Determine whether or not to place "t" in the subset
The question tells us that "t" cannot be in the subset.
So, we can complete stage 1 in 1 way (that is, we DO NOT place "t" in the subset

Stage 2: Determine whether or not to place "s" in the subset
We can either HAVE "s" in the subset or NOT HAVE "s" in the subset
So, we can complete stage 2 in 2 ways

Stage 3: Determine whether or not to place "u" in the subset
We can either HAVE "u" in the subset or NOT HAVE "u" in the subset
So, we can complete this stage in 2 ways

Stage 4: Determine whether or not to place "w" in the subset
We can either HAVE "w" in the subset or NOT HAVE "w" in the subset
So, we can complete this stage in 2 ways

Stage 5: Determine whether or not to place "x" in the subset
We can complete this stage in 2 ways

By the Fundamental Counting Principle (FCP), we can complete the 5 stages (and thus build all possible subsets) in (1)(2)(2)(2)(2) ways ([spoiler]= 16 ways = E[/spoiler])

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775