Let $l_{1}$ and $l_{2}$ be two lines intersecting at $P$. If $A_{1},\ B_{1},\ C_{1}$ are points on $l_{1}$ and $A_{2},\ B_{2},\ C_{2},\ D_{2},\ E_{2}$ are points on $l_{2}$ and if none of these coincides with $P$, then the number of triangles formed by these eight points, is

Question

Dr. Abubacker · Accepted Answer

(d)
If triangle is formed including point $'P'$ the other points must be one from $l_{1}$ and other point from $l_{2}$. Number of triangle formed with $P = {\ ^{3}C}_{1} 	imes {\ ^{5}C}_{1} = 15$ ways
When $P$ is not included.
Number of triangle formed
$= {\ ^{3}C}_{2} 	imes {\ ^{5}C}_{1} + {\ ^{3}C}_{1} 	imes {\ ^{5}C}_{2} = 15 + 15 = 30$
Total number of triangles=15+30=45

Q. Let $l_{1}$ and $l_{2}$ be two lines intersecting at $P$. If $A_{1},\ B_{1},\ C_{1}$ are points on $l_{1}$ and $A_{2},\ B_{2},\ C_{2},\ D_{2},\ E_{2}$ are points on $l_{2}$ and if none of these coincides with $P$, then the number of triangles formed by these eight points, is

Explanation

Reviewed by Dr. Abubacker

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