How many different subsets of the set {10, 14, 17, 24} are there that

Question

How many different subsets of the set {10, 14, 17, 24} are there that contain an odd number of elements?

(A) 3 
(B) 6 
(C) 8 
(D) 10 
(E) 12

PareshGmat · Answer

Answer = C = 8

{10}
{14}
{17}
{24}
{10, 14, 17}
{14, 17, 24}
{10, 17, 24}
{10, 14, 24}

HKD1710 · Answer

Choosing 1 or 3 from the 4 values will make a subset that contains an odd number.

so choose 1 out of 4 is 4c1 = 4

and choose 3 out of 4 is 4c3 = 4

total = 4+4 = 8

SergeyDudko · Answer

Is there any mistake in my sets? In my point of view they're all different. Am I right?
10, 10, 10
14, 14, 14
17, 17, 17
24, 24, 24
10, 10, 14
10, 10, 17
10, 10, 24
14, 14, 17
14, 14, 24
17, 17, 24

Sincerely,
Sergey.

aviram · Answer

Question is a little tricky to understand. There are two odd sets that can be created, namely of one and three elements each.

Set of one element: We can choose from 4 different numbers, so we have 4 choices.
Set of three elements: We can choose 3 numbers from 4 total numbers, which gives us 4C3=4

Therefore, total number sets with an odd number of elements = 8.

GMATinsight · Answer

Since, The Subsets must contain an odd umber of elements therefore the set may have either 1 element or 3 elements in the subsets

The Number of Ways in which the Subet of 1 element can be made from the set of 4 elements = 4 C 1 = 4

The Number of Ways in which the Subet of 3 elements can be made from the set of 4 elements = 4 C 3 = 4

Total Such Subsets of either 1 or 3 elements each - 4 + 4 = 8

Answer: Option C

jayanthjanardhan · Answer

Are we assuming the ordering does not matter here? As in (10,14,17) is different from (14,10,17)?...they both contain the same elements after all!

GMATinsight · Answer

While making a Subset of numbers the order is not taken into account and if the question expects the ordered pairs then it will be clearly mentioned in question.

However the ordered pair calculation will be as follows:

Subset of 1 term each = 4C1 = 4

Subset of 3 term each = 4C3*3! = 4*6=24

I.e. total subsets = 4+24=28

I hope it helps!

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How many different subsets of the set {10, 14, 17, 24} are there that

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