Solve
-There Are $n$ People in a Room $N$ Of Possible Handshakes by All the People in the Room

Multiple Choice

Solve.
-There are $n$ people in a room. The number $N$ of possible handshakes by all the people in the room is given by the function $N ( n ) = \frac { n ( n - 1 ) } { 2 }$ . For what number n of people is $91 \leq N \leq 190$ ?

A) $\{ n \mid 13 \leq n \leq 22 \}$
B) $\{ n \mid 15 \leq n \leq 19 \}$
C) $\{ \mathrm { n } \mid 16 \leq \mathrm { n } \leq 19 \}$
D) $\{ n \mid 14 \leq n \leq 20 \}$