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A={2, 4, 6, 8, 10} is given. What is the number of subsets o

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by Max@Math Revolution » Thu Aug 29, 2019 8:49 am

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[GMAT math practice question]

A={2, 4, 6, 8, 10} is given. What is the number of subsets of A containing 3 elements?

A. 5
B. 10
C. 12
D. 24
E. 32
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by deloitte247 » Sun Sep 01, 2019 12:44 pm
If every member of a new set is contained in set A, then the new set is a subset of A.
Let's have a new set C where A is the superset of the new set.
If set A has 'n' elements
$$Total\ subsets=2^n$$
*If set A has 'n' elements,
$$Total\ proper\ subsets=2^n-1$$
*If set A has 'n' elements
For total subsets with y elements = nCy
Subsets of A containing 3 elements =5C3
$$=>\frac{5!}{3!\cdot2!\cdot1!}=\frac{5\cdot4\cdot3!}{3!\cdot2\cdot1\cdot1}=\frac{20}{2}=10$$
I.e 10 subsets of A contains 3 elements

Answer = B
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by Max@Math Revolution » Sun Sep 01, 2019 9:09 pm
=>

The number of subsets is equal to the number of ways ways to choose 3 elements out of 5 elements, which is 5C3 = (5*4*3)/(1*2*3) = 10.

Therefore, B is the answer.
Answer: B
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