If one quarter of all the subsets (containing three elements) of the set A={a1,a2,a3,…,an} contains the element a3, then the value of n is
A
10
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B
12
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C
14
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D
None of these
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Solution
The correct option is B12 There are nC3 subsets of set A, containing three elements. If a3 is always included, then there are n−1C2 subsets of set A. Given, 14×nC3=n−1C2 ⇒n(n−1)(n−2)24=(n−1)(n−2)2⇒n=12