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Question
Answer the following:
There are 12 distinct points A, B, C, ....., L, in order, on a circle. Lines are drawn passing through each pair of points how many triangles have on vertex C.
Solution
If one of the vertices of the triangle is on C, then the other two vertices can be chosen from the remaining 11 points.
This can be done in 11C2 ways.
∴ the total number of triangles have vertex on C
= 11C2
= `(11!)/(2!9!)`
= `(11 xx 10)/(1 xx 2)`
= 55
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