Can someone please solve the following:
How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
A) 16
B) 27
C) 31
D) 32
E) 64
OA is D
Combinatorics problem
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 theCodeToGMAT
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(6c6 + 6c5 + 6c4 + 6c3 + 6c2 + 6c1)  (5c5 + 5c4 + 5c3 + 5c2 + 5c1)
= (1 + 6 + 3x5 + 5x4 + 3x5 + 6)  (1 + 5 + 5x2 + 5x2 + 5)
= (7 + 15 + 20 + 15 + 6)  (6 + 10 + 10 + 5)
= 63  31
= 32
= (1 + 6 + 3x5 + 5x4 + 3x5 + 6)  (1 + 5 + 5x2 + 5x2 + 5)
= (7 + 15 + 20 + 15 + 6)  (6 + 10 + 10 + 5)
= 63  31
= 32
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Here's another approach...topspin360 wrote:
How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
A) 16
B) 27
C) 31
D) 32
E) 64
Take the task of building subsets and break it into stages.
Stage 1: Determine whether or not to place "0" in the subset
The question tells us that "0" cannot be in the subset.
So, we can complete stage 1 in 1 way (that is, we DO NOT place "0" in the subset
Stage 2: Determine whether or not to place "1" in the subset
We can either HAVE "1" in the subset or NOT HAVE "1" in the subset
So, we can complete stage 2 in 2 ways
Stage 3: Determine whether or not to place "2" in the subset
We can either HAVE "2" in the subset or NOT HAVE "2" in the subset
So, we can complete this stage in 2 ways
Stage 4: Determine whether or not to place "3" in the subset
We can either HAVE "3" in the subset or NOT HAVE "3" in the subset
So, we can complete this stage in 2 ways
Stage 5: Determine whether or not to place "4" in the subset
We can complete this stage in 2 ways
Stage 6: Determine whether or not to place "5" in the subset
We can complete this stage in 2 ways
By the Fundamental Counting Principle (FCP), we can complete all 6 stages (and thus build all possible subsets ) in (1)(2)(2)(2)(2)(2) ways ([spoiler]= 32 ways = D[/spoiler])
Cheers,
Brent
Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmatcounting?id=775
Last edited by [email protected] on Sat Jan 11, 2014 4:49 pm, edited 1 time in total.

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