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
OA: C
What's wrong with options B and D?
How many different subsets of the set {10, 14, 17, 24} are t
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There's only two ways that a subset can contain an odd number of elements here (assuming that each element can only be selected once): if the set contains 1 element and if the set contains 3 elements.ardz24 wrote: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
OA: C
What's wrong with options B and D?
1 element sets: {10}, {14},{17}, {24} ---> 4 sets
3 elements sets: {10, 14, 17}, {10, 14, 24}, {10, 17, 24}, {14, 17, 24} --> 4 sets
4 + 4 = 8 sets total. The answer is C.
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Hi ardz24,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
OA: C
What's wrong with options B and D?
Let's take a look at your question.
We are asked to find the number of subsets of the set {10, 14, 17, 24} that contain an odd number of elements.
The subsets that have odd number of elements have either 1 or 3 elements.
Let's find those subsets.
Subsets with one element = {10}, {14}, {17}, {24}
Subsets with 3 elements = {10, 14, 17}, {10, 14, 24}, (10, 17, 24}, {14, 17, 24}
So there are 8 subsets that have odd number of elements.
Therefore, Option C is correct.
Hope this helps.
I am available if you'd like any follow up.
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The options are:BTGmoderatorAT wrote: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
OA: C
What's wrong with options B and D?
17
10
14
24
10, 14, 17
17, 14, 24
17, 10, 24
10, 14, 24
Alternate solution:
Fact: For a set with n elements, the number of the subsets containing r elements (where 0 ≤ r ≤ n) is nCr.
Using the above fact, the number of subsets containing 1 element is 4C1 = 4, and the number subsets containing 3 elements is 4C3 = 4. Therefore, the number of subsets containing an odd number of elements is 4 + 4 = 8.
Answer: C
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