I have a question that is: " How many subsets with more than two elements does a set with $100$ elements have? "
Can you help me understanding it step by step?
Thanks in advance .....


Hint 1: A set of $m$ elements has $\binom{m}{n}=\frac{m!}{n!(m-n)!}$, $\ n$-element subsets. So in your case you have to perform the summation of the above values for $m=100$ and $2< n\leq 100$.

Hint 2 (alternative): The total number of subsets of a $100$-elements set, is $2^{100}$. How many of them are subsets with less than two elements?

  • $\begingroup$ They are three: empty set, 1-elmt set, and 2-elmt set but, how can I get the number of 2-elmt subsets? $\endgroup$ – White159 Oct 13 '16 at 4:39
  • $\begingroup$ I meant three types of subsets .. $\endgroup$ – White159 Oct 13 '16 at 4:43
  • $\begingroup$ Read carefully my post above: the number of $2$-element subsets is $\binom{100}{2}$. $\endgroup$ – KonKan Oct 13 '16 at 5:32
  • $\begingroup$ I got it ... thanks ... but, why the order is not important here? $\endgroup$ – White159 Oct 13 '16 at 18:32
  • $\begingroup$ What do you mean "the order is not important here"? $\endgroup$ – KonKan Oct 13 '16 at 22:35

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