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Question

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 B 12
There are nC3 subsets of set A, containing three elements.
If a3 is always included, then there are n1C2 subsets of set A.
Given, 14×nC3=n1C2
n(n1)(n2)24=(n1)(n2)2n=12

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