How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
16
27
31
32
64
OA- 32
[spoiler]Can someone help me with the below logic -
Total sets without 0 =
5 (Individual sets of 1 number each - {1},{2}, etc)
5C2 (Sets of 2 numbers each)
5C3 (sets of 3 numbers each)
5C4 (sets of 4 numbers each)
5C5 (Set of 5 numbers)
= 5+10+10+5+1 = 31
(which set am i missing?)
[/spoiler][/spoiler]
Sets - counting subsets
This topic has expert replies
- snigdha1605
- Senior | Next Rank: 100 Posts
- Posts: 43
- Joined: Fri Feb 22, 2013 10:41 pm
- Thanked: 3 times
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Any of the following values may be included in a subset:snigdha1605 wrote:How many different subsets of the set {0, 1, 2, 3, 4, 5} do not contain 0?
16
27
31
32
64
OA- 32
1, 2, 3, 4, 5
For each of these values, there are 2 options: TO INCLUDE the value or NOT TO INCLUDE the value.
Since there are 5 values, and 2 options for each value, the total number of possible subsets = 2*2*2*2*2 = 32.
The correct answer is D.
The 32 options above include the EMPTY SET: the case in which NONE of the 5 values is selected.
The EMPTY SET is considered a subset of EVERY SET.
This concept is beyond the scope of the GMAT, so please feel free to ignore this problem.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
- snigdha1605
- Senior | Next Rank: 100 Posts
- Posts: 43
- Joined: Fri Feb 22, 2013 10:41 pm
- Thanked: 3 times
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
Hi snigdha1605,
I thought I'd point out that your approach of adding 5C1 + 5C2 + 5C3 etc would have worked (except you missed 5C0). Once you get to the point where you are adding all possible combinations, you can use a nice rule that says:
nC0 + nC1 + nC2 + . . . . nCn = 2^n
So, for example, 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 2^5
Similarly, 7C0 + 7C1 + 7C2 + . . . 7C6 + 7C7 = 2^7
Cheers,
Brent
I thought I'd point out that your approach of adding 5C1 + 5C2 + 5C3 etc would have worked (except you missed 5C0). Once you get to the point where you are adding all possible combinations, you can use a nice rule that says:
nC0 + nC1 + nC2 + . . . . nCn = 2^n
So, for example, 5C0 + 5C1 + 5C2 + 5C3 + 5C4 + 5C5 = 2^5
Similarly, 7C0 + 7C1 + 7C2 + . . . 7C6 + 7C7 = 2^7
Cheers,
Brent
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
5C0 represents the number of ways we can select 0 objects from a set of 5 objects. There is 1 way to accomplish this. In other words, 5C0 = 1amey90 wrote:@Brent, what doe 5C0 signify here?
5C5 means you select 5 nos from 5 or 5C1 means you select 1 no. from 5 nos.
wouldn't 5C0 would just mean a blank set?
Thanks.
Cheers,
Brent