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# M28-29

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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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16 Sep 2014, 01:29
00:00

Difficulty:

35% (medium)

Question Stats:

74% (01:13) correct 26% (01:22) wrong based on 46 sessions

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Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. $$29$$
B. $$56$$
C. $$57$$
D. $$63$$
E. $$64$$

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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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16 Sep 2014, 01:29
Official Solution:

Set S contains 7 different letters. How many subsets of set S, including an empty set, contain at most 3 letters?

A. $$29$$
B. $$56$$
C. $$57$$
D. $$63$$
E. $$64$$

1 empty set;

$$C^1_7=7$$ sets with one element;

$$C^2_7=21$$ sets with two elements;

$$C^3_7=35$$ sets with three element.

Total 1+7+21+35=64 sets.

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Joined: 05 Aug 2015
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12 Mar 2016, 14:32
Why doesn't for example AB and BA count as a different subset?? No where in the problem says that order doesn't matter.

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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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13 Mar 2016, 08:26
happyface101 wrote:
Why doesn't for example AB and BA count as a different subset?? No where in the problem says that order doesn't matter.

A set, by definition, is a collection of elements without any order. (While, a sequence, by definition, is an ordered list of terms.)
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Intern
Joined: 04 Sep 2016
Posts: 19

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03 Apr 2017, 03:24
We dont we count the empty set too? So 65?
Math Expert
Joined: 02 Sep 2009
Posts: 46291

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03 Apr 2017, 03:28
alexlovesgmat wrote:
We dont we count the empty set too? So 65?

1 empty set;

$$C^1_7=7$$ sets with one element;

$$C^2_7=21$$ sets with two elements;

$$C^3_7=35$$ sets with three element.

Total 1+7+21+35=64 sets.
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Joined: 27 Dec 2016
Posts: 231
Concentration: Marketing, Social Entrepreneurship
GPA: 3.65
WE: Marketing (Education)

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18 Sep 2017, 18:40
Bunuel, I actually do not understand what "an empty set" means. Could you please explain?

Thanks.
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Math Expert
Joined: 02 Sep 2009
Posts: 46291

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18 Sep 2017, 21:26
septwibowo wrote:
Bunuel, I actually do not understand what "an empty set" means. Could you please explain?

Thanks.

An empty set is a set which has no elements.
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Joined: 07 Oct 2015
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02 Jun 2018, 20:11
Hi Bunuel,

I was trying to solve this question by the slot method but I am not getting it right.

Since there are are 3 spaces that need to be filled, we have three slots. The first slot could have either of the 7 letters or a blank, second slot could have either of the 6 letters or a blank and so on... And since we have 3 slots, divide that by 3!.

(8*7*6)/3! = 56

The empty set should be accounted for within this as well. So, according to me, this should have been the end of it but that's wrong of course. Can you please tell me what I am missing?

Re: M28-29   [#permalink] 02 Jun 2018, 20:11
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# M28-29

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