Two members of a certain club are selected to speak at the next club meeting. If there are 66 different possible selections of the 2 club members, how many members does the club have? Choose the most appropriate option.
A) 5  B) 6  C) 7  D) 8  E) 12
Method-1   Total No. of Selection of r out of n objects are defined by nCr = n! / [(r!)(n-r)!]   i.e. If total member = n   then nC2 = n! / [(2!)(n-2)!] = 66   i.e. n*(n-1)*n-2!/ [(2!)n-2!] = 66   i.e. n*(n-1) = 132   (for Positive Values of n)   therefore, n*(n-1) = 132   i.e. n= 12   Answer: Option 12
<result>E</result>
Two members of a certain club are selected to speak at the next club meeting. If there are 66 different possible selections of the 2 club members, how many members does the club have?