The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly eight elements each?
Choices
A) 27  B) 18  C) 16  D) 8  E) 9
nC2 = 36   =&gt; n*(n-1)/2 = 36 , by middle term factor   =&gt; n = 9   nC3 = 9C8 = 9   So, Answer is 9.
<result>E</result>
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly eight elements each?