Two members of a certain club are selected to speak at the next club meeting.
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?
Answer/Solution
12
Steps/Work
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 E
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 E