If 7 points out of 12 are in the straight line, then the numbers of triangles formed by joining them is

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185

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201

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None of these

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Solution

The correct option is B
185

The number of ways of selecting 3 points out of 12 points is $12_{C_{3}}$ .
The number of ways of selecting 3 points out of 7 points on the same straight line is $7_{C_{3}}$ .
Hence the number of triangles formed will be $12_{C_{3}} - 7_{C_{3}} = 185$ .

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If 7 points out of 12 are in the straight line, then the numbers of triangles formed by joining them is

The correct option is B 185 The number of ways of selecting 3 points out of 12 points is 12C3. The number of ways of selecting 3 points out of 7 points on the same straight line is 7C3. Hence the number of triangles formed will be 12C3−7C3=185.

The correct option is B
185

The number of ways of selecting 3 points out of 12 points is $12_{C_{3}}$ .
The number of ways of selecting 3 points out of 7 points on the same straight line is $7_{C_{3}}$ .
Hence the number of triangles formed will be $12_{C_{3}} - 7_{C_{3}} = 185$ .