the set s has 36 different subsets each of which contains exactly two elements . how many subsets of s could contain exactly 7 elements each ?  Choices
A) 81  B) 63  C) 54  D) 36  E) 90

Rationale: nc 2 = 36 = > n * ( n - 1 ) / 2 = 36 by middle term factor and n can not be negative = > n = 9 nc 7 = 9 c 7 = 9 ! / 7 ! * ( 9 - 7 ) ! = 9 * 8 * 7 ! / 7 ! * 2 = 36 so , answer is d .
Answer: D