The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly seven elements each?	Choose the correct choice from the following answers: A) 81 B) 63 C) 54 D) 36 E) 90
nC2 = 36   =&gt; n*(n-1)/2 = 36 by middle term factor and n cannot be negative   =&gt; n = 9   nC7 = 9C7 = 9!/7!*(9-7)!= 9*8*7!/7!*2 =36   So, Answer is 36.
<result>D</result>
The set S has 36 different subsets each of which contains exactly two elements. How many subsets of S could contain exactly seven elements each?