There are 10 points in a plane out of which 5 are collinear. Find the number of straight lines formed by joining them.

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Solution

line is formed by joining 2 pt.s & 5
collinear pt. 1 line rather then $^{5} C_{2}$ lines
$∴$ total ways $=^{10} C_{2} -^{5} C_{2} + 1 = 45 - 10 + 1 = 36$

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There are 10 points in a plane out of which 5 are collinear. Find the number of straight lines formed by joining them.

line is formed by joining 2 pt.s & 5 collinear pt. 1 line rather then 5C2 lines∴ total ways =10C2−5C2+1=45−10+1=36

line is formed by joining 2 pt.s & 5
collinear pt. 1 line rather then $^{5} C_{2}$ lines
$∴$ total ways $=^{10} C_{2} -^{5} C_{2} + 1 = 45 - 10 + 1 = 36$