Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?  Select the correct option.
A) 20  B) 27  C) 40  D) 57  E) 95
Below is an answer to your question.   C2n=190Cn2=190 --&gt; n!/2!∗(n−2)!=190. Now, notice that n!=(n−2)!∗(n−1)∗n so (n−2)!∗(n−1)∗n2!∗(n−2)!=190 --&gt; (n−1)∗n/2=190 (n−1)n=380 --&gt; n=20   20nswer: 20.
<result>A</result>
Two members of a club are to be selected to represent the club at a national meeting. if there are 190 different possible selections of the 2 members, how many members does the club have?