The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly six elements each? Pick.
A) 96 B) 80 C) 84 D) 88 E) 92
n842 = 36   =&gt; n*(n-1)/2 = 36 by middle term factor and n cannot be negative   =&gt; n = 9   n843 = 9846 = 9!/6!*(9-6)!= 9*8*7*6!/6!*3*2 =84   So, Answer is 84.
<result>C</result>
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly six elements each?