If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?
Choose the correct choice: A) 2300 B) 600 C) 250 D) 300 E) none of these
1st line - 0 points   2nd line - new 1 point   3td line - new 2 points + old 1 point   4th line - new 3 points + old 2+1 points   5th line - new 4 points + old 3+2+1 points   n-th line - (n-1) points + (n-2) .... 3+2+1   therefore, S=1+2+3...(n-1)   S=(n-1)n/2=24*25/2= 
<gadget id="calculator">24*25/2</gadget>
<output>300</output>
300   ANS;300
<result>D</result>
If 25 lines are drawn in a plane such that no two of them are parallel and no three are concurrent, then in how many points do they intersect?