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Question
The number of triangles whose vertices are at vertices of octagon but none of whose sides happen to come from the sides of octagon
The number of triangles whose vertices are at vertices of octagon but none of whose sides happen to come from the sides of octagon
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Solution
In order to get a triangle whose sides do not coincide with that of the octagon, the vertices should be alternate.
Total no. of ways of choosing 1st vertex = 8
Total no. of ways of choosing 2nd vertex = 2 , each on either side of the 1st vertex
Total no. of ways of choosing 3rd vertex = 1
Total no. of triangles = 8*2*1 = 16
In order to get a triangle whose sides do not coincide with that of the octagon, the vertices should be alternate.
Total no. of ways of choosing 1st vertex = 8
Total no. of ways of choosing 2nd vertex = 2 , each on either side of the 1st vertex
Total no. of ways of choosing 3rd vertex = 1
Total no. of triangles = 8*2*1 = 16
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