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 is c
How can i get the correct answer here with well detailed explanation? please help me out
Thanks
set problem
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Hi Roland2rule,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 is c
How can i get the correct answer here with well detailed explanation? please help me out Crying or Very sad
Thanks
Let's take a look at your question.
The given set is: $$\left\{10,\ 14,\ 17,\ 24\right\}$$
The subsets that include odd number elements could have either one element or 3 elements. So let's first write all possible subsets that have only one element.
$$\left\{10\right\},\ \left\{14,\right\}\ \left\{17\right\},\left\{24\right\}$$
Therefore, there are 4 subsets that have one element.
Now let's write all possible subsets that have 3 elements.
$$\left\{10,\ 14,\ 17\right\},\ \left\{10,\ 14,\ 24\right\},\ \left\{10,\ 17,\ 24\right\},\ \left\{14,\ 17,\ 24\right\}$$
Therefore, there are 4 possible subsets of the given set that have 3 elements.
Hence the total number of subsets that have odd number of elements are 4 + 4 = 8.
So, Option C is correct.
Hope it helps.
I am available if you'd like any follow up.
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Solution:BTGmoderatorRO wrote: ↑Sat Oct 28, 2017 4:40 amHow 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 is c
How can i get the correct answer here with well detailed explanation? please help me out
Thanks
The options are:
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 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 of 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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