Mathematics

Problem

10 different vectors are lying on a plane out of which four are parallel with respect to each other. Probability that three vectors chosen from them will satisfy the equation

\lambda_1\mathbf{a} + \lambda_2\mathbf{b} + \lambda_3\mathbf{c} = 0

, where

\lambda_1, \lambda_2

and

\lambda_3 \neq 0

is a.

\frac{{}^6C_2 \times {}^4C_1}{{}^{10}C_3}

\frac{({}^6C_3 \times {}^4C_1) + {}^6C_3}{{}^{10}C_3}

\frac{({}^6C_2 \times {}^4C_1) + ({}^4C_3)}{{}^{10}C_3}

\frac{({}^6C_2 + {}^4C_1) + ({}^6C_2 \times {}^4C_1)}{{}^{10}C_3}

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