Sets and their families

Probability Level 2

We know that a finite set with $n$ elements has $2^{n}$ subsets. Suppose a set $A$ has 200 elements, how many two-element subsets does $A$ have?

2^{199}

20000

2^{200}

19900

1 solution

Hana Wehbi
May 16, 2016

Any set with $n$ elements has $\frac{n(n-1)}{2}$ two-element subsets. We can prove this by mathematical induction.