There are 15 points in a plane, no three of which are in a straight line, except 6, all of which are in a st. line. The number of st. lines which can be drawn by joining them is

Question

There are 15 points in a plane, no three of which are in a straight line, except 6, all of which are in a st. line. The number of st. lines which can be drawn by joining them is (A) 15C2-6  (B) 15C2- 6C2  (C) 15C2- 6C2-1  (D) 15C2- 6C2+1

Tardigrade Admin · Accepted Answer

Reqd. no. of st. lines = 15C2- 6C2+1 [∵ join of two pts. from a st. line and 6 pts. which are collinear given only st. line in place of 6c2]

Q. There are $15$ points in a plane, no three of which are in a straight line, except $6$ , all of which are in a st. line. The number of st. lines which can be drawn by joining them is

$^{15} C_{2} - 6$

$^{15} C_{2} -^{6} C_{2}$

$^{15} C_{2} -^{6} C_{2} - 1$

$^{15} C_{2} -^{6} C_{2} + 1$

Reqd. no. of st. lines $=^{15} C_{2} -^{6} C_{2} + 1$
[ $∵$ join of two pts. from a st. line and $6$ pts. which are collinear given only st. line in place of $^{6} c_{2}$ ]

Q. There are 15 points in a plane, no three of which are in a straight line, except 6, all of which are in a st. line. The number of st. lines which can be drawn by joining them is

15C2​−6

15C2​−6C2​

15C2​−6C2​−1

15C2​−6C2​+1