There are $m$ points in space, no four of which are in plane with the exception of $n$ points which are all in the same plane. The number of different planes determined by the points is

^{m} C_{3} -^{n} C_{3} + 1

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^{m + 1} C_{3} -^{n} C_{3} + 1

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^{m - 1} C_{3} +^{n} C_{3}

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^{m + 1} C_{3} -^{n} C_{3}

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Solution

The correct option is A $^{m} C_{3} -^{n} C_{3} + 1$
For defining a plane, we need $3$ points
so, number of planes that can be made from m points $=^{m} C_{3}$
but out of them $n$ points are coplanar i.e. they lie on the same plane
So, planes selected by selecting 3 points out of these n points are identical
So, number of planes $=^{m} C_{3} -^{n} C_{3} + 1$ (+1 indicates the plane that is formed by those n points which is removed by our subtraction)

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There are m points in space, no four of which are in plane with the exception of n points which are all in the same plane. The number of different planes determined by the points is

There are $m$ points in space, no four of which are in plane with the exception of $n$ points which are all in the same plane. The number of different planes determined by the points is