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Question

A set contains 2n+1 elements. The number of subsets of this set containing more than n elements is equal to

A
2n1
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B
2n
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C
2n+1
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D
22n
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Solution

The correct option is D 22n
Let the original set contains (2n+1) elements, then subsets of this set containing more than n elements, i.e., subsets containing (n+1) elements, (n+2) elements,....(2n+1) elements.
Required number of subsets
=2n+1Cn+1+2n+1Cn+2+...+2n+1C2n+2n+1C2n+1
=2n+1Cn+2n+1Cn1+...+2n+1C1+2n+1C0
=2n+1C0+2n+1C1+2n+1C2+...+2n+1Cn1+2n+1Cn
=12[(1+1)2n+1]=12[22n+1]=22n.

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