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Question

How many subsets of a set with $100$ elements have more than $2$ element?

Approach

Number of subsets of a set with $100$ elements =$2^{100}$

Number of subsets of a set with $100$ elements having more than $2$ element

=$2^{100}$-Number of subsets of a set with $100$ elements having less than $2$ element$(X)$

$X$=Number of subsets of a set with $100$ elements having no element $( \phi) $+ Number of subsets of a set with $100$ elements having one element =1+100

Hence,

Number of subsets of a set with $100$ elements having more than $2$ element=

$2^{100}-101$

Am I right?

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You are wrong. You forgot to include sets with exactly two elements.

The correct formula would be

Number of subsets = Number of sets with more than 2 elements + number of sets with 2 elements + number of sets with less than 2 elements.

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    $\begingroup$ will the answer be $2^{100}-101-\binom{100}{2}$ =$2^{100}-101-4950$ ? isn't it? $\endgroup$ – laura May 11 '17 at 12:27
  • $\begingroup$ @laura Yup, that's the answer! $\endgroup$ – 5xum May 11 '17 at 12:28

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