P_1 and P_2 are two distinct and intersecting planes. Three non-c… - Vidyadip

Question

$P_1$ and $P_2$ are two distinct and intersecting planes. Three non-collinear points lie on $P_1$ and another three non-collinear points lie on $P_2$ (none being on line of intersection of planes). Then the maximum number of tetrahedrons formed using these six points, is

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Answer

b
Required number of tetrahedrons

$ = \,{}^3{C_3}\, \times \,{}^3{C_1} + {}^3{C_2} \times {}^3{C_2} + {}^3{C_1} \times {}^3{C_3} = 15$

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